Connectivity keeping edges of trees in 3-connected or 3-edge-connected graphs

Qing Yang; Yingzhi Tian

Connectivity keeping edges of trees in 3-connected or 3-edge-connected graphs

Combinatorics 2023-03-08 v1

Authors: Qing Yang , Yingzhi Tian

Abstract

Hasunuma [J. Graph Theory 102 (2023) 423-435] conjectured that for any tree $T$ of order $m$ , every $k$ -connected (or $k$ -edge-connected) graph $G$ with minimum degree at least $k+m-1$ contains a tree $T'\cong T$ such that $G-E(T')$ is still $k$ -connected (or $k$ -edge connected). Hasunuma verified this conjecture for $k\leq 2$ . In this paper, we confirm this conjecture for $k=3$ .

Keywords

graph connectivity tree connectivity keeping edges 3-connected graph 3-edge-connected graph minimum degree

Cite

@article{arxiv.2303.03896,
  title  = {Connectivity keeping edges of trees in 3-connected or 3-edge-connected graphs},
  author = {Qing Yang and Yingzhi Tian},
  journal= {arXiv preprint arXiv:2303.03896},
  year   = {2023}
}

Connectivity keeping edges of trees in 3-connected or 3-edge-connected graphs

Abstract

Keywords

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