Spanning trees of claw-free graphs with few leaves and branch vertices

TL;DR

This paper investigates the properties of spanning trees with limited leaves and branch vertices in claw-free graphs, providing new bounds and improvements over previous results in this area.

Contribution

It introduces new bounds on spanning trees with few leaves and branch vertices specifically for claw-free graphs, advancing understanding in this graph class.

Findings

Established bounds on leaves and branch vertices in spanning trees of claw-free graphs

Improved previous results on spanning trees with few branch vertices in claw-free graphs

Applied main results to enhance existing theorems in the literature

Abstract

Let $T$ be a tree. A vertex of degree one is a \emph{leaf} of $T$ and a vertex of degree at least three is a \emph{branch vertex} of $T$. A graph is said to be claw-free if it does not contain $K_{1,3}$ as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of claw-free graphs. Applying the main results, we also give some improvements of previous results on the spanning trees with few branch vertices for the case of claw-free graphs.