Vertex disjoint copies of K1,4 in claw-free graphs

Yun Wang, Suyun Jiang and Jin Yan

Applied Mathematics and Computation, 2021, vol. 393, issue C

Abstract: A complete bipartite graph with partite sets X and Y, where |X|=1 and |Y|=r, is denoted by K1,r. A graph G is said to be claw-free if G does not contain K1,3 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 K1,4s in claw-free graphs. Let k be an integer with k≥2 and let G be a claw-free graph with |V(G)|≥10k−9. We prove that if the minimum degree of G is at least 4, then it contains k vertex disjoint K1,4s. This result answers the question in [Jiang, Chiba, Fujita, Yan, Discrete Math. 340 (2017) 649–654].

Keywords: Claw-free; Minimum degree; Disjoint subgraphs (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307219

DOI: 10.1016/j.amc.2020.125768

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