Graph factors and factorization: 1985--2003: a survey
From MaRDI portal
Publication:868347
DOI10.1016/j.disc.2005.11.059zbMath1112.05088OpenAlexW2068431006WikidataQ62638537 ScholiaQ62638537MaRDI QIDQ868347
Publication date: 2 March 2007
Published in: Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.disc.2005.11.059
Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)
Related Items
Assessing the Computational Complexity of Multi-layer Subgraph Detection, Sufficient conditions for the existence of pseudo 2-factors without isolated vertices and small odd cycles, Sharp upper bounds on the minimum number of components of 2-factors in claw-free graphs, An overview of graph covering and partitioning, A neighborhood condition for graphs to have restricted fractional (g,f)-factors, Construction of k-matchings in graph products, Partitioning a Graph into Highly Connected Subgraphs, An Extension of Cui-Kano's Characterization on Graph Factors, Approximation and Exact Algorithms for Special Cases of Connected f-Factors, A note on semi-coloring of graphs, Sufficient condition for the existence of an even \([a,b\)-factor in graph], \(P_3\)-factors in the square of a tree, Regular colorings in regular graphs, Factorizations of the product of cycles, Degree sequences and the existence of \(k\)-factors, Optimal identification of sets of edges using 2-factors, On the complexity landscape of connected \(f\)-factor problems, Improved degree conditions for 2-factors with \(k\) cycles in Hamiltonian graphs, NP-hardness of two edge cover generalizations with applications to control and bribery for approval voting, \(P_k\)-factors in squares and line graphs of trees, Binding number and path-factor critical deleted graphs, Isolated toughness and path-factor uniform graphs. II., Latin hexahedra and related combinatorial structures, The existence of even regular factors of regular graphs on the number of cut edges, Optimal embeddings of the exchanged hypercube and the dual-cube as vertex-induced subgraphs of the hypercube, Packing $k$-Matchings and $k$-Critical Graphs, Subdigraphs with orthogonal factorizations of digraphs, Matchings with lower quotas: algorithms and complexity, Uniform Lie algebras and uniformly colored graphs, On caterpillar factors in graphs, Stability number and \(f\)-factors in graphs, Unnamed Item, Packing bipartite graphs with covers of complete bipartite graphs, Spanning trees: A survey, On specific factors in graphs, A sufficient condition for the existence of restricted fractional \((g, f)\)-factors in graphs, On the complexity of deciding whether the regular number is at most two, Nash-Williams conditions for the existence of all fractional \([a,b\)-factors], Perfect matchings and \(K_{1,p}\)-restricted graphs, Degree-bounded factorizations of bipartite multigraphs and of pseudographs, Algorithmic complexity of weakly semiregular partitioning and the representation number, Path factors and parallel knock-out schemes of almost claw-free graphs, SEMIREGULAR FACTORIZATIONS OF REGULAR MULTIGRAPHS, Edge-disjoint Hamilton cycles in graphs, Computing Sharp 2-Factors in Claw-Free Graphs, An algorithm for computing simple \(k\)-factors, Computing sharp 2-factors in claw-free graphs, Induced claws and existence of even factors of graphs, Latin squares with no small odd plexes, Component factors of the Cartesian product of graphs, Bipartite toughness and \(k\)-factors in bipartite graphs, Minimum degree, independence number and pseudo \([2, b\)-factors in graphs], On path factors of \((3,4)\)-biregular bigraphs, Editing to Connected F-Degree Graph, Some results about component factors in graphs, Degree conditions for fractional \((a,b,k)\)-critical covered graphs, Improved queue-size scaling for input-queued switches via graph factorization, Connected \(k\)-factors in bipartite graphs, On Cui-Kano's Characterization Problem on Graph Factors, The existence of path-factor covered graphs, On \(P_{\geq 3}\)-factor deleted graphs
Cites Work
- On factors with given components
- [a,b-factors of graphs]
- Regular subgraphs of almost regular graphs
- The complexity of computing the permanent
- On the relationship between the genus and the cardinality of the maximum matchings of a graph
- Minimum degree of bipartite graphs and the existence of k-factors
- A simple existence criterion for \((g<f)\)-factors
- Three-regular parts of four-regular graphs
- Partition of graphs with condition on the connectivity and minimum degree
- Maximum graphs with a unique k-factor
- Critical graphs, matchings and tours or a hierarchy of relaxations for the travelling salesman problem
- Regular factors in nearly regular graphs
- On certain classes of fractional matchings
- Every 4-regular graph plus an edge contains a 3-regular subgraph
- On circuits in graphs
- A generalization of Tutte's 1-factor theorem to countable graphs
- Sufficient conditions for a graph to have factors
- Structure theorem and algorithm on \((1,f)\)-odd subgraph
- The complexity of regular subgraph recognition
- Factorizations of regular graphs
- An extension of matching theory
- A note on the complexity of finding regular subgraphs
- On factors with all degrees odd
- Faktoren in unendlichen Graphen. (Factors in infinite graphs)
- Factors of regular graphs
- The number of matchings in random regular graphs and bipartite graphs
- Maximal tight sets and the Edmonds-Gallai decomposition for matchings
- Matching theory
- Recent progress on edge-colouring graphs
- Fractional matchings and the Edmonds-Gallai theorem
- Matchings in infinite graphs
- The general maximum matching algorithm of Micali and Vazirani
- The linear arboricity of graphs
- Factors and induced subgraphs
- 1-factorizing regular graphs of high degree - an improved bound
- On the number of edge-disjoint one factors and the existence of \(k\)-factors in complete multipartite graphs
- F-factors of graphs: A generalized matching problem
- On generalized matching problems
- Graph factorization, general triple systems, and cyclic triple systems
- On factors in random graphs
- Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix
- The solution of van der Waerden's problem for permanents
- Some problems about linear arboricity
- Packing subgraphs in a graph
- Canonical edge-colourings of locally finite graphs
- Graph factors
- One-factor in random graphs based on vertex choice
- A sufficient condition for a graph to have \([a,b\)-factors]
- An Ore-type condition for the existence of \(k\)-factors in graphs
- One-factors and \(k\)-factors
- Infinite matching theory
- Decomposing infinite graphs
- \(f\)-optimal factors of infinite graphs
- Binding numbers and \(f\)-factors of graphs
- On the strength of König's duality theorem for infinite bipartite graphs
- Star arboricity
- On the number of 1-factorizations of the complete graph
- Matchings in graphs. II
- On defect-d matchings in graphs
- Injective choice functions for countable families
- Decomposition of \(K_n\) into subgraphs of prescribed type
- An extension of Tutte's 1-factor theorem
- Connected factors in \(K_{1,n}\)-free graphs containing a \((g,f)\)-factor
- A degree condition for the existence of \([a,b\)-factors in \(K_{1,n}\)-free graphs]
- Vertex-disjoint claws in graphs
- On connected factors in \(K_{1,3}\)-free graphs
- On 2-factors in claw-free graphs
- Odd factors of a graph
- Extending matchings in graphs: A survey
- A theory of alternating paths and blossoms for proving correctness of the \(O(\sqrt{V}E)\) general graph maximum matching algorithm
- Complexity of the hamiltonian cycle in regular graph problem
- Matchable infinite graphs
- Complete bipartite factorisations by complete bipartite graphs
- Edge coloring regular graphs of high degree
- Connected \([k,k+1\)-factors of graphs]
- A characterization of graphs having all \((g,f)\)-factors
- Optimal packing of induced stars in a graph
- Neighborhood conditions and \(k\)-factors
- Counting 1-factors in regular bipartite graphs
- Graph decompositions without isolated vertices. II
- The k-factor conjecture is true
- Advances on the Hamiltonian problem -- a survey
- A necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two
- On regular factors in regular graphs with small radius
- On unique \(k\)-factors and unique \([1,k\)-factors in graphs.]
- Complete factors and \(f\)-factors
- On the bipartite case of El-Zahár's conjecture
- More sufficient conditions for a graph to have factors
- Regular factors of simple regular graphs and factor-spectra
- A neighbourhood condition for graphs to have \([a,b\)-factors]
- Connected \([a,b\)-factors in graphs]
- Odd subgraphs and matchings
- Connected factors in graphs -- a survey
- Complete bipartite factorisations of \(K _{n,n}\)
- Simplified existence theorems for \((g,f)\)-factors
- On barrier sets of star-factors
- Toughness of graphs and the existence of factors
- On f-factors of a graph
- König-Egerváry graphs, 2-bicritical graphs and fractional matchings
- Isomorphic factorization of r-regular graphs into r parts
- Degree conditions for Hamiltonian graphs to have \([a,b\)-factors containing a given Hamiltonian cycle]
- Spanning subgraphs with specified valencies
- Valencies of graphs with 1-factors
- Subgraphs of graphs. I
- On a 2-factor with a specified edge in a graph satisfying the Ore condition
- Regular factors in regular multipartite graphs
- On neighborhood condition for graphs to have [\(a\), \(b\)-factors]
- A neighborhood condition for graphs to have \([a, b\)-factors. II]
- Graph decompositions without isolated vertices
- Regular graphs, regular factors, and the impact of Petersen's theorems
- Sufficient conditions for graphs to have \((g,f)\)-factors
- On the complexity of some edge-partition problems for graphs
- Rounding in symmetric matrices and undirected graphs
- Vertex-disjoint cycles containing specified edges
- Decomposition of graphs into \((g,f)\)-factors
- \((r,r+1)\)-factorizations of \((d,d+1)\)-graphs
- Strong transfinite version of König's duality theorem
- Disjoint factors of diameter two in complete graphs
- Tough graphs and Hamiltonian circuits.
- Algorithms for constructing graphs and digraphs with given valences and factors
- Decompositions of complete bipartite and tripartite graphs into selfcomplementary factors with finite diameters
- Efficient Algorithms for Petersen's Matching Theorem
- 2-factors in claw-free graphs
- On packing 3-vertex paths in a graph
- Balanced network flows. IV. Duality and structure theory
- Unique Maximum Matching Algorithms
- Connected (g, f)-factors
- Unique maximum matching algorithms
- A note concerning graphs with unique f-factors
- Binding number and minimum degree for k-factors
- On the Complexity of General Graph Factor Problems
- Dynamic matchings and quasidynamic fractional matchings. II
- On the Problem of Decomposing a Graph into n Connected Factors
- Isomorphic factorizations VII. Regular graphs and tournaments
- Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree
- Path factors in cubic graphs
- Graph decomposition with constraints on the connectivity and minimum degree
- Isomorphic factorizations of complete equipartite graphs
- A General Criterion for the Existence of Transversals
- Factors and factorizations of graphs—a survey
- One-factorizations of the complete graph—A survey
- [a,b-factorization of a graph]
- Packings by Complete Bipartite Graphs
- Toughness and the existence ofk-factors
- Complexité de l'arboricité linéaire d'un graphe II
- Regular factors of regular graphs
- Factorizations of regular graphs of high degree
- BINDING NUMBERS OF GRAPHS AND THE EXISTENCE OF k-FACTORS
- Some results on linear arboricity
- Two sufficient conditions for a 2-factor in a bipartite graph
- k -Factors and Neighbourhoods of Independent Sets in Graphs
- Some results on odd factors of graphs
- Some conditions for the existence off-factors
- On Restricted Two-Factors
- The Complexity of Enumeration and Reliability Problems
- Perfect triangle-free 2-matchings
- A remark on the factor theorems of lovász and tutte
- The NP-Completeness of Some Edge-Partition Problems
- The NP-Completeness of Edge-Coloring
- Graph decomposition: A new key to coding theorems
- Covering and packing in graphs IV: Linear arboricity
- Integer and Fractional Matchings
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Perfect matchings in random s‐uniform hypergraphs
- Almost Every Graph can be Covered by Linear Forests
- Perfect Matchings in Random r-regular, s-uniform Hypergraphs
- Star-factors andk-bounded total domination
- Component factors and induced subgraphs
- Edge-Coloring Bipartite Graphs
- An algorithmic proof of Tutte's f-factor theorem
- Paths, Trees, and Flowers
- Some Properties of Graphs with Multiple Edges
- On the completeness of a generalized matching problem
- Subgraphs with prescribed valencies
- On the existence of a factor of degree one of a connected random graph
- COVERING AND PACKING IN GRAPHS, I.
- Sufficient conditions for matchings
- On the maximal number of independent circuits in a graph
- A sufficient condition for a bipartite graph to have a k‐factor
- The Factorization of Linear Graphs
- Distinct representatives of subsets
- FACTORIZATION OF EVEN GRAPHS
- The Factors of Graphs
- A Short Proof of the Factor Theorem for Finite Graphs
- Injective choice functions
- Three‐regular subgraphs of four‐regular graphs
- Linear arboricity and linear \(k\)-arboricity of regular graphs
- Graph colouring and the probabilistic method
- The overfull conjecture and the conformability conjecture
- Factors and connected induced subgraphs
- All regular multigraphs of even order and high degree are 1-factorable
- Fractional \((g,f)\)-factors of graphs
- Path factors in claw-free graphs
- A \([k,k+1\)-factor containing a given Hamiltonian cycle]
- On a conjecture of bollobás and bosák
- Linear arboricity of random regular graphs
- Updating the hamiltonian problem—A survey
- [a,b‐factorizations of graphs]
- Regular factors in K1,n free graphs
- Regular Multigraphs of High Degree are 1-Factorizable
- A degree condition for the existence ofk-factors
- Decomposition of Complete Graphs into Isomorphic Factors with a Given Diameter
- On the Computational Complexity of Combinatorial Problems
- Matchings in Countable Graphs
- On Factors of a Graph
- 1-Factors and Antifactor Sets
- The Planar Hamiltonian Circuit Problem is NP-Complete
- Isomorphic Factorisations. I: Complete Graphs
- Matchings in infinite graphs
- A homology theory for spanning tress of a graph
- A bibliographic survey of edge‐colorings
- Convexity of degree sequences
- Bipartite Edge Coloring in $O(\Delta m)$ Time
- Faster scaling algorithms for general graph matching problems
- The Numbers of Spanning Trees, Hamilton Cycles and Perfect Matchings in a Random Graph
- Graph decompositions without isolated vertices III
- Degree conditions for 2-factors
- Decomposing 4-Regular Graphs into Triangle-Free 2-Factors
- Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture
- Two‐factors each component of which contains a specified vertex
- Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at leastk
- On the structure of graphs with a uniquek-factor
- K4−‐factor in a graph
- Balanced network flows. III. Strongly polynomial augmentation algorithms
- Closure, 2-factors, and cycle coverings in claw-free graphs
- Almost‐regular factorization of graphs
- Independence number, connectivity, and r‐factors
- Isomorphic Factorization of Regular Graphs and 3-Regular Multigraphs
- König's Duality Theorem for Infinite Bipartite Graphs
- Embedding k -Regular Graphs in k + 1-Regular Graphs
- A review of random graphs
- On Representatives of Subsets
- Paths in graphs
- Finding 1-Factors in Bipartite Regular Graphs and Edge-Coloring Bipartite Graphs
- The fractional matching numbers of graphs
- Vertex‐disjoint cycles containing prescribed vertices
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item