Restricted unimodular chordal graphs

• Published in: Journal of graph theory Vol. 30; no. 2; pp. 121 - 136
• Main Authors: Peled, Uri N., Wu, Julin
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.02.1999
• Subjects: balanced bipartite graphs; chordal graphs; ptolemaic graphs; totally unimodular matrices
• ISSN: 0364-9024; 1097-0118
• DOI: 10.1002/(SICI)1097-0118(199902)30:2<121::AID-JGT6>3.0.CO;2-1

A chordal graph is called restricted unimodular if each cycle of its vertex‐clique incidence bipartite graph has length divisible by 4. We characterize these graphs within all chordal graphs by forbidden induced subgraphs, by minimal relative separators, and in other ways. We show how to construct them by starting from block graphs and multiplying vertices subject to a certain restriction, which leads to a linear‐time recognition algorithm. We show how they are related to other classes such as distance‐hereditary chordal graphs and strongly chordal graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 121–136, 1999