Vertex-Disjoint \(K_{1,t}\)’s in Graphs

Abstract

Let \(\delta(G)\) denote the minimum degree of a graph \(G\). We prove that for \(t \geq 4\) and \(k \geq 2\), a graph \(G\) of order at least \((t + 1)k + 2t^2 – 4t + 2\) with \(\delta(G) \geq k+t- 1\) contains \(k\) pairwise vertex-disjoint \(K_{1,t}\)’s.