Hereditary Nordhaus–Gaddum graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED Discrete Applied Mathematics Pub Date : 2025-02-13 DOI:10.1016/j.dam.2025.02.010

Vaidy Sivaraman , Rebecca Whitman

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引用次数: 0

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

G

satisfy

χ (H) + χ (\bar{H}) \geq | 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.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.

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