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A graph G is called claw-free if G has no induced subgraph isomorphic to K 1,3 . We prove that if G is a claw-free graph with minimum degree at least d, then G has a path factor such that the order of each path is at least d+1.
In this paper, we present several conditions for K 1,3 -free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K 1,3 -free graph with a minimum degree sum δ2>2 3n+1−4; every {K 1,3 ,P 7 }-free graph with δ 2 ⩾9; every {K 1,3 ,Z 4 }-free graph with δ 2 ⩾9; and every K 1,3 -free graph with maximum...
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