Work

Hereditary Nordhaus–Gaddum graphs

Year: 2025

Type: article

Abstract: Nordhaus and Gaddum proved in 1956 that the sum of the chromatic number χ of a graph G and its complement is at most | G | + 1 . The Nordhaus–Gaddum graphs are the class of graphs satisfying this inequality with equality, and are well-understood. In this paper we consider a hereditary generalization: graphs G for which all induced subgraphs H of G satisfy χ ( H ) + χ ( H ¯ ) ≥ | H | . We characterize the forbidden induced subgraphs of this class and find its intersection with a number of common classes, including line graphs. We also discuss χ -boundedness and algorithmic results.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2025.02.010

Authors: Vaidy Sivaraman, Rebecca Whitman

Institutions: Mississippi State University, University of California, Berkeley

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: $3,090

OpenAlex ID: W4407429633

FWCI:

Cites: 20

Cited by:

Related to: 10