Hamilton cycles in 5-connected line graphs

DOI10.1016/j.ejc.2011.09.015zbMath1239.05113arXiv1009.3754OpenAlexW2014937299MaRDI QIDQ412285

Tomáš Kaiser, Petr Vrána

Publication date: 4 May 2012

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.3754

zbMATH Keywords

conjecture of Carsten Thomassen

Mathematics Subject Classification ID

Paths and cycles (05C38) Connectivity (05C40) Eulerian and Hamiltonian graphs (05C45)

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Cites Work

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• Hamiltonicity of 6-connected line graphs
• On hamiltonian line graphs and connectivity
• Contractible subgraphs, Thomassen's conjecture and the dominating cycle conjecture for snarks
• On a closure concept in claw-free graphs
• Edge-disjoint trees containing some given vertices in a graph
• On decomposing a hypergraph into \(k\) connected sub-hypergraphs
• Equivalence of Fleischner's and Thomassen's conjectures
• Eulerian subgraphs and Hamilton-connected line graphs
• Every 3-connected, essentially 11-connected line graph is Hamiltonian
• Every 4-connected line graph of a quasi claw-free graph is Hamiltonian connected
• Line graphs of multigraphs and Hamilton-connectedness of claw-free graphs
• On the Problem of Decomposing a Graph into n Connected Factors
• Edge-Disjoint Spanning Trees of Finite Graphs
• Hamiltonian results inK1,3-free graphs
• Cycles Intersecting Edge-Cuts of Prescribed Sizes
• Edge disjoint Steiner trees in graphs without large bridges
• Indecomposabler-graphs and some other counterexamples
• Reflections on graph theory
• On Eulerian and Hamiltonian Graphs and Line Graphs
• Hamilton connectivity of line graphs and claw‐free graphs