A note on spanning trees of connected $K_{1,t}$-free graphs whose stems have a few leaves

Pham Hoang Ha; Dang Dinh Hanh

A note on spanning trees of connected $K_{1,t}$-free graphs whose stems have a few leaves

Combinatorics 2018-10-22 v1

Authors: Pham Hoang Ha , Dang Dinh Hanh

Abstract

Let $T$ be a tree, a vertex of degree one is called a leaf. The set of leaves of $T$ is denoted by $Leaf(T)$ . The subtree $T-Leaf(T)$ of $T$ is called the stem of $T$ and denoted by $Stem(T).$ In this note, we give a sharp sufficient condition to show that a $K_{1,t}-$ free graph has a spanning tree whose stem has a few leaves. By applying the main result, we give improvements of previous related results.

Keywords

spanning tree k1,t-free graph stem leaf sufficient condition connected graph

Cite

@article{arxiv.1810.08336,
  title  = {A note on spanning trees of connected $K_{1,t}$-free graphs whose stems have a few leaves},
  author = {Pham Hoang Ha and Dang Dinh Hanh},
  journal= {arXiv preprint arXiv:1810.08336},
  year   = {2018}
}

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