Forbidden Pairs for Vertex-Disjoint Claws
نویسنده
چکیده
Let k ≥ 4, and let H1, H2 be connected graphs with |V (Hi)| ≥ 3 for i = 1, 2. A graph G is said to be {H1, . . . , Hl}-free if none of H1, . . . , Hl is an induced subgraph of G. We prove that if there exists a positive integer n0 such that every {H1, H2}-free graph G with |V (G)| ≥ n0 and δ(G) ≥ 3 contains k vertex-disjoint claws, then {H1, H2} ∩ {K1,t | t ≥ 2} = ∅. Also, we prove that every K1,rfree graph of sufficiently large order with minimum degree at least t contains k vertex-disjoint copies of K1,t.
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