منابع مشابه
Hamilton-connected indices of graphs
Let G be an undirected graph that is neither a path nor a cycle. Clark and Wormald [L.H. Clark, N.C. Wormald, Hamiltonian-like indices of graphs, ARS Combinatoria 15 (1983) 131–148] defined hc(G) to be the least integerm such that the iterated line graph Lm(G) is Hamilton-connected. Let diam(G) be the diameter of G and k be the length of a longest path whose internal vertices, if any, have degr...
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A graph G is k-Hamilton-connected (k-hamiltonian) if G−X is Hamilton-connected (hamiltonian) for every setX ⊂ V (G) with |X| = k. In the paper, we prove that (i) every 5-connected claw-free graph with minimum degree at least 6 is 1Hamilton-connected, (ii) every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with...
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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.
متن کاملEulerian subgraphs and Hamilton-connected line graphs
Let C(l, k) denote a class of 2-edge-connected graphs of order n such that a graph G ∈ C(l, k) if and only if for every edge cut S ⊆ E(G) with |S| ≤ 3, each component of G − S has order at least n− k l . We prove the following. (1) If G ∈ C(6, 0), then G is supereulerian if and only if G cannot be contracted to K2,3, K2,5 or K2,3(e), where e ∈ E(K2,3) and K2,3(e) stands for a graph obtained fro...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2012
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.291.574