Disjoint stars and forbidden subgraphs
Disjoint stars and forbidden subgraphs
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DOI：
10.32917/hmj/1171377081
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发表时间：
2006-11
影响因子：
0.2
通讯作者：
S. Fujita
中科院分区：
文献类型：
--
作者：
S. Fujita
设r， k为r≥3，k≥2的整数。证明了如果G是一个至少（k−1）(2r−1)+ 1阶且δ(G)≥2的K1，rfree图，则G包含k个K1,2的顶点不相交副本。这一结果的动机是刻画了一个禁忌子图H，它满足“每一个足够大阶且最小度至少为t的无H图包含k个顶点不相交的星K1，t的副本”的表述。在本文中，我们也给出了这个问题的答案。
Let r, k be integers with r ≥ 3, k ≥ 2. We prove that if G is a K1,rfree graph of order at least (k − 1)(2r − 1) + 1 with δ(G) ≥ 2, then G contains k vertex-disjoint copies of K1,2. This result is motivated by characterizing a forbidden subgraph H which satisfies the statement “every H-free graph of sufficiently large order with minimum degree at least t contains k vertex-disjoint copies of a star K1,t”. In this paper, we also give the answer of this problem.