Partitions of graphs into chain graphs & co.

27^th March 2024, 13:00 Ashton Lecture Theatre
Dr. Bogdan Alecu
School of Computing, University of Leeds

Abstract

An undirected simple graph is a {\em chain graph} if it is bipartite, and for each part, the neighbourhoods of the vertices in that part can be ordered linearly with respect to inclusion (or equivalently, if it is bipartite, and does not contain $2K_2$ -- the complement of a chordless cycle on 4 vertices -- as an induced subgraph).

In this talk, we will explore some parameters related to partitioning graphs into chain graphs (and some appropriately defined ``complements''). We will discuss the motivation behind these parameters, which originated in the world of permutation patterns on the one hand, and in the study of well-quasi-orderability under induced subgraphs on the other. We will then go through various results surrounding the parameters, and present several open problems.