Remarks on path-factor critical avoidable graphs

Abstract

Zhou (2023) introduced the concept of path-factor critical avoidable graph and determined several parameter bounds for (P≥2,n) or (P≥3,n)-factor critical avoidable graphs. Certain instances are listed in Zhou (2023) to show that these toughness or isolated toughness bounds are sharp. However, the derivation processes are flawed. In this remark, we directly modify the derivation processes and obtain the revised bounds. The counterexamples are updated to satisfy κ(G)=n+2. Finally, richness bounds on binding number for a graph to be path-factor critical avoidable are determined.

Keywords

• 05C70
• 05C38