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arXiv · 2201.01043

Spanning trees of $K_{1,4}$-free graphs with a bounded number of leaves and branch vertices

Pham Hoang Ha
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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 \emph{$K_{1,4}$-free} if it does not contain $K_{1,4}$ as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of $K_ {1,4}$-free graphs. Applying the main results, we also give some improvements of previous results on the spanning tree with few branch vertices for the case of $K_{1,4}$-free graphs.

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Pham Hoang Ha. 2022-01-04. Spanning trees of $K_{1,4}$-free graphs with a bounded number of leaves and branch vertices. https://arxiv.org/abs/2201.01043

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