Spanning trees of $K_{1,4}$-free graphs whose reducible stems have few leaves

Pham Hoang Ha; Le Dinh Nam; Ngoc Diep Pham

Spanning trees of $K_{1,4}$-free graphs whose reducible stems have few leaves

Combinatorics 2023-05-15 v1

Authors: Pham Hoang Ha , Le Dinh Nam , Ngoc Diep Pham

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 $T$ . The {\it reducible stem } of $T$ is the smallest subtree that contains all branch vertices of $T$ . In this paper, we give some sharp sufficient conditions for $K_{1,4}$ -free graphs to have a spanning tree whose reducible stem having few leaves.

Keywords

spanning tree k_{1,4}-free graph reducible stem branch vertex leaf sufficient condition

Cite

@article{arxiv.2305.07232,
  title  = {Spanning trees of $K_{1,4}$-free graphs whose reducible stems have few leaves},
  author = {Pham Hoang Ha and Le Dinh Nam and Ngoc Diep Pham},
  journal= {arXiv preprint arXiv:2305.07232},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2112.04102

Spanning trees of $K_{1,4}$-free graphs whose reducible stems have few leaves

Abstract

Keywords

Cite

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