INDUCED REGULAR PERFECT GRAPHS

Gokul S Jayakumar; Sangeetha V

doi:10.56827/SEAJMMS.2023.1903.23

Gokul S Jayakumar Department of Mathematics, CHRIST (Deemed to be University), Bangalore- 560029, Karnataka, INDIA
Sangeetha V Department of Mathematics, CHRIST (Deemed to be University), Bangalore- 560029, Karnataka, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2023.1903.23

Keywords: Perfect graphs, F-perfect graphs, Regular graphs, Rperfect graphs, Graph minors.

Abstract

A graph G is said to be R-perfect if, for all induced subgraphs H of G, the induced regular independence number of each induced subgraph H is equal to its corresponding induced regular cover. Here, the induced regular independence number is the maximum number of vertices in H such that no two belong to the same induced regular subgraph in H, and the induced regular cover of H is the minimum number of induced regular subgraphs in H required to cover the vertex set of H. This article introduces the notion of induced regular perfect graphs or R-perfect graphs through which we study the structural properties of R-perfect graphs and identify a forbidden class of graphs for the same. This further leads to the characterization of R-perfect biconnected graphs. With these results, we derive and prove a general characterization for R-perfect graphs.