Some Results on Path-Factor Critical Avoidable Graphs

• Published in: Discussiones Mathematicae. Graph Theory Vol. 43; no. 1; pp. 233 - 244
• Main Author: Zhou, Sizhong
• Format: Journal Article
• Language: English
• Published: Sciendo 01.02.2023; University of Zielona Góra
• Subjects: (p≥k,n)-factor critical avoidable graph; 05C38; 05C70; 90B10; factor; factor critical avoidable graph; graph; isolated toughness; p≥k-factor; toughness
• ISSN: 1234-3099; 2083-5892
• DOI: 10.7151/dmgt.2364

A path factor is a spanning subgraph of such that every component of is a path with at least two vertices. We write = { : ≥ }. Then a -factor of means a path factor in which every component admits at least vertices, where ≥ 2 is an integer. A graph is called a -factor avoidable graph if for any ∈ ), admits a -factor excluding . A graph is called a ( , )-factor critical avoidable graph if for any ( ) with | | = , − is a -factor avoidable graph. Let be an ( + 2)-connected graph. In this paper, we demonstrate that (i) is a ( )-factor critical avoidable graph if ; (ii) is a ( )-factor critical avoidable graph if ; (iii) is a ( )-factor critical avoidable graph if ; (iv) is a ( )-factor critical avoidable graph if . Furthermore, we claim that these conditions are sharp.