Spanning trees with at most 2 branch vertices in claw - free graphs

Pham Hoang Ha; Dang Dinh Hanh

Spanning trees with at most 2 branch vertices in claw - free graphs

Combinatorics 2018-11-06 v2

Authors: Pham Hoang Ha , Dang Dinh Hanh

Abstract

In this article, we will prove that if $G$ is a connected claw-free graph and either $\sigma_6(G)\geq |G|-5$ or $\sigma_7(G)\geq |G|-2$ , here $\sigma_k(G)$ is the minimmum degree sum of $k$ independent vertices in $G$ , then $G$ has a spanning tree with at most two branch vertices.

Keywords

claw-free graphs spanning tree branch vertices degree sum independent vertices

Cite

@article{arxiv.1806.00734,
  title  = {Spanning trees with at most 2 branch vertices in claw - free graphs},
  author = {Pham Hoang Ha and Dang Dinh Hanh},
  journal= {arXiv preprint arXiv:1806.00734},
  year   = {2018}
}

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