科研之友
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摘要
A graph G is N-m-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. In this note, we first present a counterexample to the conjecture that every 3-connected, N-2-locally connected claw-free graph is hamiltonian and then show that both connected N-2-locally connected claw-free graph and connected N-3-locally connected claw-free graph with minimum degree at least three have connected even [2, 4]-factors.
