Forbidden pairs and the existence of a dominating cycle

TL;DR

This paper investigates conditions involving forbidden pairs that ensure the existence of a dominating cycle in 2-connected graphs, contributing to the understanding of cycle domination under specific constraints.

Contribution

It introduces new forbidden pair conditions that guarantee the presence of a dominating cycle in 2-connected graphs, advancing graph theory knowledge.

Findings

Identifies specific forbidden pairs that guarantee dominating cycles

Provides proofs for the existence of dominating cycles under these conditions

Enhances understanding of cycle domination in constrained graph classes

Abstract

A cycle in a graph is called dominating if every edge of the graph is incident with a vertex of the cycle. In this paper, we investigate forbidden pairs guaranteeing the existence of a dominating cycle in 2-connected graphs.