Note on Hamilton Circuits

From MaRDI portal
Publication:3264678

DOI10.2307/2308928zbMath0089.39505OpenAlexW2035089435WikidataQ55891930 ScholiaQ55891930MaRDI QIDQ3264678

Øystein Ore

Publication date: 1960

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2308928



Related Items

Forbidden pairs and \((k,m)\)-pancyclicity, Heavy subgraphs, stability and Hamiltonicity, Improved sufficient conditions for \(k\)-leaf-connected graphs, Closures, cycles, and paths, Extremal problems on consecutive \(L(2,1)\)-labelling, On Hamiltonian bipartite graphs, Characterizing forbidden pairs for relative length of longest paths and cycles, Fan-type implicit-heavy subgraphs for Hamiltonicity of implicit claw-heavy graphs, On the 3-color Ramsey numbers \(R(C_4,C_4,W_n)\), Degree sums and spanning brooms of a graph, Geodesic-pancyclic graphs, Spanning Cycles Through Specified Edges in Bipartite Graphs, An efficient condition for a graph to be Hamiltonian, An Ore-type analogue of the Sauer-Spencer theorem, Connectivity, traceability and Hamiltonicity, The neighborhood union of independent sets and hamiltonicity of graphs, More aspects of arbitrarily partitionable graphs, Strengthened Ore conditions for \((s, t)\)-supereulerian graphs, Minimum degree conditions for the strength and bandwidth of graphs, Unnamed Item, Bipartite independent number and Hamilton-biconnectedness of bipartite graphs, Stability theorems for graph vulnerability parameters, Hamiltonian paths, unit-interval complexes, and determinantal facet ideals, Maximum properly colored trees in edge-colored graphs, Proper connection and size of graphs, Some local-global phenomena in locally finite graphs, Long cycles through specified vertices, A note on degree sum conditions for 2-factors with a prescribed number of cycles in bipartite graphs, Transversals and bipancyclicity in bipartite graph families, Sufficient conditions for graphs to be spanning connected, On Saito's conjecture and the Oberly-Sumner conjectures, Partial degree conditions and cycle coverings in bipartite graphs, An implicit degree sum condition for cycles through specified vertices, A sharp Ore-type condition for a connected graph with no induced star to have a Hamiltonian path, Hyper-Hamiltonicity in graphs: some sufficient conditions, Online search for a hyperplane in high-dimensional Euclidean space, On hyper-Hamiltonicity in graphs, A note on spanning trees with a specified degree sequence, Edge degrees and dominating cycles, Color degree sum conditions for properly colored spanning trees in edge-colored graphs, Partitioning the vertices of a digraph into directed cycles and degenerated directed cycles, An improvement of sufficient condition for \(k\)-leaf-connected graphs, Degree sequence conditions for a graph to be disjoint path coverable, Disjoint long cycles in a graph, Recent advances on the Hamiltonian problem: survey III, On implicit heavy subgraphs and Hamiltonicity of 2-connected graphs, Notes on vertex pancyclicity of graphs, Edge disjoint caterpillar realizations, New sufficient condition for Hamiltonian graphs, Spanning trees with few leaves, An Ore-type theorem on equitable coloring, Generalizations of the classics to spanning connectedness, Relative length of longest paths and longest cycles in triangle-free graphs, On spanning connected graphs, Sufficient Ore type condition for a digraph to be supereulerian, Long cycles containing \(k\)-ordered vertices in graphs, Degree conditions on claws and modified claws for Hamiltonicity of graphs, Degree sum and connectivity conditions for dominating cycles, Stability of arc-transitive graphs, On a spanning \(k\)-tree in which specified vertices have degree less than \(k\), Maxima of the \(Q\)-index: forbidden even cycles, On 2-edge-connected \([\mathbf{a,b}\)-factors of graphs with Ore-type condition], On the degrees of a strongly vertex-magic graph, Sufficient conditions for a graph to be Hamiltonian, Fan-type theorem for long cycles containing a specified edge, Toughness in graphs -- a survey, Nowhere-zero 3-flows and \(Z_{3}\)-connectivity of a family of graphs, New local conditions for a graph to be Hamiltonian, Spanning bipartite graphs with high degree sum in graphs, 2-connected Hamiltonian claw-free graphs involving degree sum of adjacent vertices, Partitioning 2-Edge-Colored Ore-Type Graphs by Monochromatic Cycles, Sparsity of integer formulations for binary programs, Pancyclic graphs. I, On traceability of claw-\({o_{-1}}\)-heavy graphs, On k-path Hamiltonian graphs and line-graphs, On the edit distance of powers of cycles, Finding long cycles in balanced tripartite graphs: a first step, An Ore-type condition for Hamiltonicity in tough graphs, Energy conditions for Hamiltonicity of graphs, Angular bisector insertion algorithm for solving small-scale symmetric and asymmetric traveling salesman problem, Hamiltonian \(s\)-properties and eigenvalues of \(k\)-connected graphs, Disjoint cycles and \(2\)-factors with Fan-type condition in a graph, Une condition suffisante d'existence d'un circuit Hamiltonien dans un graphe oriente, Theory of path length distributions. I, Fractional matching preclusion number of graphs, Covering cycles and \(k\)-term degree sums, Vertex degree sums for matchings in 3-uniform hypergraphs, Forcing spanning subgraphs via Ore type conditions, Spectral radius and the 2-power of Hamilton cycle, Partitioning a graph into a cycle and a sparse graph, Ore-type conditions for the existence of even \([2,b\)-factors in graphs], Disjoint cycles with partial degree conditions in claw-free graphs, A fan-type condition for cyclability, On \(k\)-path pancyclic graphs, Improved sufficient conditions for Hamiltonian properties, Results and problems on chorded cycles: a survey, 2-proper partition of a graph, Characterizing heavy subgraph pairs for pancyclicity, Degree sum condition for \(k\)-ordered Hamiltonian connected graphs, On independent doubly chorded cycles, The number of disjoint perfect matchings in semi-regular graphs, A degree sum condition on the order, the connectivity and the independence number for Hamiltonicity, Hamiltonian cycles in n‐extendable graphs, Circumferences of k-connected graphs involving independence numbers, Cycles of Given Size in a Dense Graph, Chvátal–Erdős Theorem: Old Theorem with New Aspects, New Ore-Type Conditions for H-Linked Graphs, Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups, Partitioning a Graph into Highly Connected Subgraphs, Understanding chicken walks on n × n grid: Hamiltonian paths, discrete dynamics, and rectifiable paths, A new sufficient condition for a Digraph to be Hamiltonian-A proof of Manoussakis Conjecture, Approximation and Exact Algorithms for Special Cases of Connected f-Factors, Vertex pancyclicity over lexicographic products, Degree Conditions for Spanning Brooms, On the 1-fault hamiltonicity for graphs satisfying Ore's theorem and its generalization, Some Hamiltonian Properties of One-Conflict Graphs, Spectral radius and spanning trees of graphs, Local Dirac's condition on the existence of 2-factor, Degree sum condition on distance 2 vertices for Hamiltonian cycles in balanced bipartite graphs, Ore- and Pósa-type conditions for partitioning 2-edge-coloured graphs into monochromatic cycles, Cycles of many lengths in Hamiltonian graphs, On sufficient conditions for spanning structures in dense graphs, Minimum degree ensuring that a hypergraph is Hamiltonian-connected, Rainbow structures in a collection of graphs with degree conditions, Unnamed Item, Cyclability, connectivity and circumference, 2-Trees: Structural insights and the study of Hamiltonian paths, Ramsey-Turán type results for matchings in edge colored graphs, On \((2, k)\)-Hamilton-connected graphs, Progress on sufficient conditions for a graph to have a spanning \(k\)-ended tree, A study on thek-ordered hamiltonian graphs, A sufficient condition for vertex bipancyclicity in balanced bipartite graphs, A Short Proof of the Hajnal–Szemerédi Theorem on Equitable Colouring, On Directed 2-factors in Digraphs and 2-factors Containing Perfect Matchings in Bipartite Graphs, On Degree Sequences Forcing The Square of a Hamilton Cycle, Sufficient Conditions for a Connected Graph to Have a Hamiltonian Path, Unnamed Item, Old Hamiltonian Ideas from a New Point of View, A Dirac-Type Result on Hamilton Cycles in Oriented Graphs, Unnamed Item, Unnamed Item, Embedding Graphs into Larger Graphs: Results, Methods, and Problems, An Implicit Degree Condition for Cyclability in Graphs, A sufficient condition for 𝑘-path Hamiltonian digraphs, COMPARISON OF SUFFICIENT DEGREE BASED CONDITIONS FOR HAMILTONIAN GRAPH, Spanning paths and cycles in triangle-free graphs, Embedding Spanning Bipartite Graphs of Small Bandwidth, Graphs and Ideals Generated by Some 2-Minors, Spectral radius and Hamiltonicity of graphs, An Ore-type condition for arbitrarily vertex decomposable graphs, Partitions of a graph into paths with prescribed endvertices and lengths, Hamiltonian cycles and 2-dominating induced cycles in claw-free graphs, An Ore-type condition for arbitrarily vertex decomposable graphs, Maximum graphs non-Hamiltonian-connected from a vertex, Fan type condition and characterization of Hamiltonian graphs, Spectral radius and Hamiltonicity of graphs, Unnamed Item, Edge disjoint Hamilton cycles in graphs, An Ore-type condition for cyclability, Unnamed Item, An asymptotic version of a conjecture by Enomoto and Ota, Some Topics in Graph Theory, Various results on the toughness of graphs, Degree conditions for weakly geodesic pancyclic graphs and their exceptions, Unnamed Item, Stabilizing Weighted Graphs, On relative length of longest paths and cycles, An approximate version of Jackson’s conjecture, Unnamed Item, Unnamed Item, Embedding Graphs Having Ore-Degree at Most Five, On a Goodman – Hedetniemi Sufficient Condition for the Graph Hamiltonicity, Sufficient Conditions for a Digraph to be Supereulerian, Highly Irregular, Hamiltonian Extension, Spanning k-ended trees of 3-regular connected graphs, Degree Conditions and Degree Bounded Trees, Hamiltonian cycles and paths through matchings, Long cycles in graphs and digraphs, Surface Embedding of Non-Bipartite $k$-Extendable Graphs, Vertex pancyclic graphs, On \(k\)-ordered graphs involved degree sum, Subgraphs, closures and hamiltonicity, On k-leaf-connected graphs, Spanning spiders and light-splitting switches, Neighborhood unions and Hamiltonian properties, New sufficient conditions for bipancyclic bipartite graphs, On one extension of Dirac's theorem on Hamiltonicity, A common generalization of Chvátal-Erdös' and Fraisse's sufficient conditions for hamiltonian graphs, A proof of a conjecture about \(D_ \lambda\)-paths in graphs with large neighborhood unions, Dirac's minimum degree condition restricted to claws, Hamiltonicity in balanced \(k\)-partite graphs, A generalization of Bondy's and Fan's sufficient conditions for Hamiltonian graphs, Cycles through prescribed vertices with large degree sum, A note on the computation on the k-closure of a graph, Degree sum conditions on two disjoint cycles in graphs, Two vertex-disjoint cycles in a graph, Extremal problems on the Hamiltonicity of claw-free graphs, On degree sum conditions for 2-factors with a prescribed number of cycles, Small cycles in Hamiltonian graphs, Degree sum conditions for Hamiltonicity on \(k\)-partite graphs, Orthogonal \([k-1,k+1\)-factorizations in graphs], Connected graph \(G\) with \(\sigma_2(G) \geq \frac{2}{3} n\) and \(K_{1, 4}\)-free contains a Hamiltonian path, Neighbourhood unions and Hamiltonian properties in graphs, Some panconnected and pancyclic properties of graphs with a local Ore-type condition, Extensions and consequences of Chvátal-Erdös' theorem, Contagious sets in dense graphs, Graphs containing every 2-factor, Hamiltonian numbers in oriented graphs, Dense arbitrarily vertex decomposable graphs, The hidden algorithm of Ore's theorem on Hamiltonian cycles, Pancyclic graphs and a conjecture of Bondy and Chvatal, On the difference between Hamilton cycles and 2-factors with a prescribed number of cycles, New Ore's type results on hamiltonicity and existence of paths of given length in graphs, Leaf number and Hamiltonian \(C_4\)-free graphs, Strong matching preclusion number of graphs, Minimum graphs with complete k-closure, A vertex cover with chorded 4-cycles, On path-coverings and Hamilton-connectivity of finite graphs, A sufficient condition for a graph to be Hamiltonian, Maximale Kreise in Graphen, Degree conditions for the existence of vertex-disjoint cycles and paths: a survey, Conditions for graphs to be path partition optimal, Structural properties and hamiltonicity of neighborhood graphs, The existence of \(f\)-forests and \(f\)-trees in graphs, Note on 2-connected graphs with \(d(u)+d(v)\geq n-4\), HybridHAM: a novel hybrid heuristic for finding Hamiltonian cycle, Existence of dominating cycles and paths, More powerful closure operations on graphs, Spanning paths in graphs, Hamiltonicity of claw-free graphs and Fan-type conditions, Hamiltonism, degree sum and neighborhood intersections, Stable properties of graphs, Degree sum and graph linkage with prescribed path lengths, An Ore-type condition for the existence of \(k\)-factors in graphs, Hamiltonian properties of graphs with large neighborhood unions, Signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree, A condition for a Hamiltonian bipartite graph to be bipancyclic, Compatible Eulerian circuits in Eulerian (di)graphs with generalized transition systems, Covering a graph with cycles of length at least 4, Neighborhood unions and a generalization of Dirac's theorem, Chorded pancyclicity in \(k\)-partite graphs, Enomoto and Ota's conjecture holds for large graphs, Extending vertex and edge pancyclic graphs, A localization method in Hamiltonian graph theory, One sufficient condition for Hamiltonian graphs involving distances, On degree sum conditions for directed path-factors with a specified number of paths, Hamiltonian jump graphs, Hamiltonian graphs involving neighborhood intersections, Number of vertices of degree three in spanning 3-trees in square graphs, Minimum degree and size conditions for the proper connection number of graphs, Existenz von Gerüsten mit vorgeschriebenem Maximalgrad in Graphen, Placing specified vertices at precise locations on a Hamiltonian cycle, On some Ramsey numbers for quadrilaterals versus wheels, A method in graph theory, Panconnected graphs. II, A generalization of implicit Ore-condition for Hamiltonicity of \(k\)-connected graphs, Degree conditions for \(k\)-Hamiltonian \([a,b\)-factors], An Ore-type condition implying a digraph to be pancyclic, A remark on two sufficient conditions for Hamilton cycles, Selecting and covering colored points, A generalization of Fan's condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness, Closure and spanning trees with bounded total excess, Degree sums, \(k\)-factors and Hamilton cycles in graphs, Spanning bipartite graphs with large degree sum in graphs of odd order, The H-force sets of the graphs satisfying the condition of Ore's theorem, Degree sum condition for the existence of spanning \(k\)-trees in star-free graphs, Neighborhood unions and cyclability of graphs, On the circumference of a graph and its complement, A degree sum condition with connectivity for relative length of longest paths and cycles, Some Ore-type conditions for the existence of connected \([2,k\)-factors in graphs], On the extremal number of edges in Hamiltonian connected graphs, 2-factors and Hamiltonicity, Proof of a conjecture of Haeggkvist on cycles and independent edges, Locally pancyclic graphs, A closure concept based on neighborhood unions of independent triples, A generalization of Ore's Theorem involving neighborhood unions, A degree characterisation of pancyclicity, Extremal problems and generalized degrees, Extending matchings in graphs: A survey, Ramsey number of paths and connected matchings in Ore-type host graphs, A sufficient local degree condition for Hamiltonicity in locally finite claw-free graphs, Note on semi-linkage with almost prescribed lengths in large graphs, An improved degree based condition for Hamiltonian cycles, Clique-heavy subgraphs and pancyclicity of 2-connected graphs, On a degree sequence analogue of Pósa's conjecture, On a \(k\)-tree containing specified leaves in a graph, Hamiltonian type properties in claw-free \(P_5\)-free graphs, An Ore-type theorem on Hamiltonian square cycles, On the cycle spectrum of cubic Hamiltonian graphs, Degree conditions for Hamiltonicity: counting the number of missing edges, A generalization of Dirac's theorem on cycles through \(k\) vertices in \(k\)-connected graphs, An implicit degree condition for pancyclicity of graphs, A \(k\)-tree containing specified vertices, Cycle lengths in Hamiltonian graphs with a pair of vertices having large degree sum, Degree bounded spanning trees, Edge bounds in nonhamiltonian \(k\)-connected graphs, Subdivision extendibility, An implicit degree Ore-condition for pancyclicity of graphs, Ore- and Fan-type heavy subgraphs for Hamiltonicity of 2-connected graphs, Generalizations of Dirac's theorem in Hamiltonian graph theory -- a survey, Algorithms for long paths in graphs, \(k\)-factors and Hamilton cycles in graphs, Spanning \(k\)-ended trees of bipartite graphs, Degree sum conditions for the circumference of 4-connected graphs, Hamilton cycles in implicit claw-heavy graphs, Ore's condition for completely independent spanning trees, Hamiltonian cycles with all small even chords, A survey on Hamilton cycles in directed graphs, Cycle lengths of Hamiltonian \(P_\ell\)-free graphs, Generalized pancyclic properties in claw-free graphs, Ramsey numbers of \(C_4\) versus wheels and stars, Spanning trees homeomorphic to a small tree, Ore-type degree conditions for disjoint path covers in simple graphs, Degree condition and \(Z_3\)-connectivity, Long cycles in unbalanced bipartite graphs, Improved degree conditions for Hamiltonian properties, An implicit degree condition for Hamiltonian graphs, On a neighborhood condition implying the existence of disjoint complete graphs, Endpoint extendable paths in dense graphs, Cycle spectra of Hamiltonian graphs, Spanning trees with small degrees and few leaves, On the 1-fault Hamiltonicity for graphs satisfying Ore's theorem, Some localization theorems on Hamiltonian circuits, The Ramsey numbers \(R(C_m,K_7)\) and \(R(C_7,K_8)\), \(\alpha\)-degree closures for graphs, Characterizing degree-sum maximal nonhamiltonian bipartite graphs, Spanning trees: A survey, Spanning \(k\)-trees of \(n\)-connected graphs, A 2-factor with short cycles passing through specified independent vertices in graph, Note on Enomoto and Ota's conjecture for short paths in large graphs, Long paths with endpoints in given vertex-subsets of graphs, Ore-condition and \(Z_3\)-connectivity, Spanning \(k\)-forests with large components in \(K_{1,k+1}\)-free graphs, Hamiltonian-connected graphs, Implicit degree condition for Hamiltonicity of 2-heavy graphs, Local connectivity, local degree conditions, some forbidden induced subgraphs, and cycle extendability, Computation of the 0-dual closure for hamiltonian graphs, Degree conditions restricted to induced paths for Hamiltonicity of claw-heavy graphs, No-hole \((r+1)\)-distant colorings, An approximate Ore-type result for tight Hamilton cycles in uniform hypergraphs, Vertex pancyclicity and new sufficient conditions, The \(k\)-dominating cycles in graphs, Degree with neighborhood conditions and highly Hamiltonian graphs, Hamiltonicity of 4-connected graphs, Algorithm for two disjoint long paths in 2-connected graphs, Conditional fault hamiltonian connectivity of the complete graph, On the number of disjoint perfect matchings of regular graphs with given edge connectivity, On degree sum conditions for long cycles and cycles through specified vertices, Ore-type versions of Brooks' theorem, A new sufficient condition for Hamiltonian graphs, Removable matchings and Hamiltonian cycles, Pancyclic graphs and linear forests, Heavy cycles in 2-connected triangle-free weighted graphs, A degree sum condition concerning the connectivity and the independence number of a graph, Extending cycles in graphs, Hamiltonian cycles and dominating cycles passing through a linear forest, Hamilton cycles in claw-heavy graphs, Degree condition for the existence of a \(k\)-factor containing a given Hamiltonian cycle, Degree conditions for the partition of a graph into cycles, edges and isolated vertices, Degree conditions and degree bounded trees, A degree condition implying that every matching is contained in a Hamiltonian cycle, On the spanning fan-connectivity of graphs, A comprehensive analysis of degree based condition for Hamiltonian cycles, On Hamiltonian cycles and Hamiltonian paths, Minimum path cover in quasi-claw-free graphs, Disjoint Hamiltonian cycles in bipartite graphs, Trees through specified vertices, Dirac's type sufficient conditions for hamiltonicity and pancyclicity, A degree sum condition for graphs to be prism Hamiltonian, Ore-type and Dirac-type theorems for matroids, Signless Laplacian spectral radius and Hamiltonicity, Connected graphs as subgraphs of Cayley graphs: conditions on hamiltonicity, Hamilton cycles and paths in vertex-transitive graphs-current directions, Ore-type conditions implying 2-factors consisting of short cycles, A look at cycles containing specified elements of a graph, An Ore-type condition for the existence of two disjoint cycles, Two theorems on Hamiltonian graphs, New sufficient conditions for cycles in graphs, Four sufficient conditions for hamiltonian graphs