Work

A Note on Lovász Characterization of Perfect Graphs

Year: 2026

Type: article

Abstract: ABSTRACT A graph is perfect if, for every induced subgraph, the chromatic number equals the size of its largest clique. In 1972, Lovász established a fundamental characterization of perfect graphs, showing that a graph is perfect if and only if, for every induced subgraph, the product of the size of the largest independent set and the size of the largest clique is at least the number of vertices. His proof relied on the technique of vertex replication. In this paper, we present an alternative proof of Lovász's result that avoids vertex replication. As vertex replication does not in general preserve ‐perfection, the argument developed here applies to the study of ‐perfect graphs, a class introduced by Ravindra in 2011.

Source: Journal of Graph Theory

DOI: 10.1002/jgt.70120

Author: James Alex

Institution: Curtin University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funder: Curtin University of Technology