Vertices missed by longest paths or circuits

DOI10.1016/0097-3165(74)90025-9zbMath0259.05120OpenAlexW2162263336MaRDI QIDQ2560260

Branko Grünbaum

Publication date: 1974

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(74)90025-9

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (25)

Cubic maximal nontraceable graphs ⋮ Planar lattice graphs with Gallai's property ⋮ Intersecting longest paths ⋮ On a conjecture of Grünbaum on longest cycles ⋮ On the hamiltonicity of a planar graph and its vertex‐deleted subgraphs ⋮ Improved upper bounds on longest-path and maximal-subdivision transversals ⋮ Planar Hypohamiltonian Graphs on 40 Vertices ⋮ Intersecting longest cycles in Archimedean tilings ⋮ K₂‐Hamiltonian graphs: II ⋮ Non-empty intersection of longest paths in \(H\)-free graphs ⋮ Improved bounds for hypohamiltonian graphs ⋮ Leaf-Critical and Leaf-Stable Graphs ⋮ Longest cycles in r-regular r-connected graphs ⋮ Highly non-concurrent longest paths in lattices ⋮ Gallai's question and constructions of almost hypotraceable graphs ⋮ Planar and infinite hypohamiltonian and hypotraceable graphs ⋮ Über längste Wege und Kreise in Graphen ⋮ Nonempty intersection of longest paths in series-parallel graphs ⋮ Planar cubic hypohamiltonian and hypotraceable graphs ⋮ Infinite families of 2-hypohamiltonian/2-hypotraceable oriented graphs ⋮ On r-regular r-connected non-hamiltonian graphs ⋮ On Hypohamiltonian and Almost Hypohamiltonian Graphs ⋮ Sublinear Longest Path Transversals ⋮ $K_2$-Hamiltonian Graphs: I ⋮ Destroying longest cycles in graphs and digraphs

Cites Work

• Non-Hamiltonian cubic planar maps
• A two-connected planar graph without concurrent longest paths
• A Theorem on Planar Graphs
• An Infinite Class of Hypohamiltonian Graphs
• On Detours in Graphs¹
• Über die Nichtexistenz eines Knotenpunktes, durch den alle längsten Wege eines Graphen gehen
• Über die Nichtexistenz zweier Knotenpunkte eines Graphen, die alle längsten Kreise fassen
• Polytopes, graphs, and complexes
• Variations on the Hamiltonian Theme
• Flip-Flops in Hypohamiltonian Graphs
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