This research aims to explore the existence of vertex-disjoint copies of K1,t in graphs with certain minimum degree conditions.
Defined minimum degree conditions for graphs G
Proved existence of vertex-disjoint copies for varying t and k
Analyzed graph order requirements for specific cases
Established conditions for the existence of k pairwise vertex-disjoint copies of K1,t
Showed that graphs of order at least (t + 1)k + 11 - 6t2 can meet these conditions
Proved results hold for t ≥ 4 and k ≥ 2
Abstract
Let (G) denote the minimum degree of a graph G.We prove that for t 4 and k 2, a graph G of order at least (t + 1)k + 11 6 t 2 with (G) k + t -1 contains k pairwise vertex-disjoint copies of K1,t.