Thomassen's conjecture implies polynomiality of 1-Hamilton-connectedness in line graphs

DOI10.1002/jgt.20578zbMath1242.05157OpenAlexW2152540681WikidataQ123002454 ScholiaQ123002454MaRDI QIDQ2891038

Petr Vrána, Roman Kužel, Zdeněk Ryjáček

Publication date: 13 June 2012

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jgt.20578

zbMATH Keywords

Hamiltonianline graphsnarkHamilton-connectedThomassen's conjecture4-connecteddominating cycle

Mathematics Subject Classification ID

Paths and cycles (05C38) Planar graphs; geometric and topological aspects of graph theory (05C10) Connectivity (05C40) Eulerian and Hamiltonian graphs (05C45)

Related Items (8)

Thomassen's conjecture for line graphs of 3-hypergraphs ⋮ How many conjectures can you stand? A survey ⋮ A Closure for 1‐Hamilton‐Connectedness in Claw‐Free Graphs ⋮ Hamiltonian properties of polyhedra with few 3-cuts. A survey ⋮ 2-edge-Hamiltonian-connectedness of 4-connected plane graphs ⋮ Ons-Hamiltonian Line Graphs ⋮ Linear‐Time Algorithms for Scattering Number and Hamilton‐Connectivity of Interval Graphs ⋮ Equivalence of Jackson's and Thomassen's conjectures

Cites Work

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• On some conjectures on cubic 3-connected graphs
• Contractible subgraphs, Thomassen's conjecture and the dominating cycle conjecture for snarks
• A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs
• The edge Hamiltonian path problem is NP-complete
• On a closure concept in claw-free graphs
• Equivalence of Fleischner's and Thomassen's conjectures
• Eulerian subgraphs and Hamilton-connected line graphs
• A note about the dominating circuit conjecture
• Reflections on graph theory
• On Eulerian and Hamiltonian Graphs and Line Graphs

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