A Hereditary Generalization of the Nordhaus-Gaddum Graphs (Rebecca Whitman)

Series
Graph Theory Seminar
Time
Tuesday, November 12, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rebecca Whitman – University of California Berkeley – https://math.berkeley.edu/people/grad/rebecca-whitman
Organizer
Evelyne Smith-Roberge

 Nordhaus and Gaddum proved in 1956 that the sum of the chromatic number  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 that the sum of the chromatic numbers of H and its complement are at least |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 chi-boundedness and algorithmic results.