Listing chordal graphs and interval graphs

Masashi Kiyomi, Shuji Kijima, Takeaki Uno

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)


We propose three algorithms for enumeration problems; given a graph G, to find every chordal supergraph (in Kn) of G, to find every interval supergraph (in Kn) of G, and to find every interval subgraph of G in Kn. The algorithms are based on the reverse search method. A graph is chordal if and only if it has no induced chordless cycle of length more than three. A graph is an interval graph if and only if it has an interval representation. To the best of our knowledge, ours are the first results about the enumeration problems to list every interval subgraph of the input graph and to list every chordal/interval supergraph of the input graph in polynomial time. The time complexities of the first algorithm is O((n + m)2) for each output graph, and those for the rest two algorithms are O(n3) for each output graph, where m is the number of edges of input graph G. We also show that a straight-forward depth-first search type algorithm is not appropriate for these problems.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540483810, 9783540483816
Publication statusPublished - 2006
Externally publishedYes
Event32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006 - Bergen, Norway
Duration: Jun 22 2006Jun 24 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4271 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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