Contractible Subgraphs of Contraction Critically Quasi $5$-Connected Graphs

Shuai Kou; Chengfu Qin; Weihua Yang

Contractible Subgraphs of Contraction Critically Quasi $5$-Connected Graphs

Combinatorics 2022-07-27 v1

Authors: Shuai Kou , Chengfu Qin , Weihua Yang

Abstract

Let $G$ be a contraction critically quasi $5$ -connected graph on at least $14$ vertices. If there is a vertex $x\in V_{4}(G)$ such that $G[N_{G}(x)]\cong K_{1,3}$ or $G[N_{G}(x)]\cong C_{4}$ , then $G$ has a quasi $5$ -contractible subgraph $H$ such that $0<\|V(H)\|<4$ .

Keywords

contraction critically quasi 5-connected graph quasi 5-contractible subgraph graph theory vertex neighborhood

Cite

@article{arxiv.2207.13047,
  title  = {Contractible Subgraphs of Contraction Critically Quasi $5$-Connected Graphs},
  author = {Shuai Kou and Chengfu Qin and Weihua Yang},
  journal= {arXiv preprint arXiv:2207.13047},
  year   = {2022}
}

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15 pages

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