Premium
Clique‐cutsets beyond chordal graphs
Author(s) -
Boncompagni Valerio,
Penev Irena,
Vušković Kristina
Publication year - 2019
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22428
Subject(s) - chordal graph , combinatorics , mathematics , indifference graph , bounding overwatch , split graph , vertex (graph theory) , cograph , clique sum , pathwidth , discrete mathematics , graph , 1 planar graph , line graph , computer science , artificial intelligence
Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (eg, the class of perfect graphs and the class of even‐hole‐free graphs), appearing both as excluded configurations, and as configurations around which graphs can be decomposed. In this paper, we study the structure of graphs that contain (as induced subgraphs) no Truemper configurations other than (possibly) universal wheels and twin wheels. We also study several subclasses of this class. We use our structural results to analyze the complexity of the recognition, maximum weight clique, maximum weight stable set, and optimal vertex coloring problems for these classes. Furthermore, we obtain polynomial χ ‐bounding functions for these classes.