What is between chordal and weakly chordal graphs?

Elad Cohen, Martin Charles Golumbic, Marina Lipshteyn, Michal Stern

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a tree T, such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [∞, ∞, 1] = [3,3,1] = [3,3,2] graphs (notation of ∞ here means that no restriction is imposed). We investigate the complete bipartite graph K 2,n and prove new theorems characterizing those K 2,n graphs that have an (h,s,2)-representation and those that have an (h,s,3)-representation. We characterize [3,2,4] graphs as equivalent to the 4-flower-free [2,4,4] graphs and give a recognition algorithm for [2,3,4] graphs. Based on these characterizations, we present new results that confirm that weakly chordal graphs, as opposed to chordal graphs, can not be characterized within the [h,s,t] framework. Furthermore, we show a hierarchy of families of graphs between chordal and weakly chordal within the [h,s,t] framework.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers
Number of pages12
StatePublished - 2008
Event34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 - Durham, United Kingdom
Duration: 30 Jun 20082 Jul 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5344 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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