Abstract A complete bipartite graph with partite sets X and Y , where | X | = 1 and | Y | = r , is denoted by K 1 , r . A graph G is said to be claw-free if G does not contain K 1 , 3 as an induced subgraph. There are several well-known and important families of graphs that are claw-free such as line graphs and complements of triangle-free graphs. Claw-free graphs have numerous interesting properties and applications. This paper considers vertex disjoint K 1 , 4 s in claw-free graphs. Let k be an integer with k ≥ 2 and let G be a claw-free graph with | V ( G ) | ≥ 10 k − 9 . We prove that if the minimum degree of G is at least 4, then it contains k vertex disjoint K 1 , 4 s. This result answers the question in [Jiang, Chiba, Fujita, Yan, Discrete Math. 340 (2017) 649–654].

中文翻译：

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无爪图中 K1,4 的顶点不相交副本

Abstract 一个具有分集 X 和 Y 的完整二分图，其中 | X | = 1 和 | 是 | = r , 由 K 1 , r 表示。如果图 G 不包含 K 1 , 3 作为诱导子图，则称图 G 是无爪图。有几个著名且重要的无爪图系列，例如折线图和无三角图的补集。无爪图具有许多有趣的特性和应用。本文考虑了无爪图中的顶点不相交 K 1 , 4 s。令 k 为 k ≥ 2 的整数，令 G 为无爪图，其中 | V ( G ) | ≥ 10 k − 9 。我们证明，如果 G 的最小度数至少为 4，则它包含 k 个不相交的顶点 K 1 , 4 s。这个结果回答了[Jiang, Chiba, Fujita, Yan, Discrete Math. 340 (2017) 649–654]。