Hamilton cycles in 5-connected line graphs
classification
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keywords
connectedlinegraphsconjecturegraphhamiltoniancarstenclaw-free
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A conjecture of Carsten Thomassen states that every 4-connected line graph is hamiltonian. It is known that the conjecture is true for 7-connected line graphs. We improve this by showing that any 5-connected line graph of minimum degree at least 6 is hamiltonian. The result extends to claw-free graphs and to Hamilton-connectedness.
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