What question did this study set out to answer?

This research aims to explore the existence of vertex-disjoint copies of K1,t in graphs with certain minimum degree conditions.

April 3, 2026Open Access

Vertex-disjoint t-claws in graphs

Key Points

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.

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Cite This Study

Shuya Chiba (Mon,) studied this question.

synapsesocial.com/papers/69cf58cb5a333a8214609a8e https://doi.org/https://doi.org/10.20604/00001137

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