Tight Toughness and Isolated Toughness for \K₂,C_n\-factor critical avoidable graph

2024/06/25 by Guan, Xiaxia, Ma, Hongxia, Wang, Maoqun
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.17631

Abstract

A spannning subgraph F of G is a \K₂,C_n\-factor if each component of F is either K₂ or C_n. A graph G is called a (\K₂,C_n\,n)-factor critical avoidable graph if G-X-e has a \K₂,C_n\-factor for any S⊆ V(G) with |X|=n and e∈ E(G-X). In this paper, we first obtain a sufficient condition with regard to isolated toughness of a graph G such that G is \K₂,C_n\-factor critical avoidable. In addition, we give a sufficient condition with regard to tight toughness and isolated toughness of a graph G such that G is \K₂,C_2i+1|i \geqslant 2\-factor critical avoidable respectively.

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