TY - GEN

T1 - Listing chordal graphs and interval graphs

AU - Kiyomi, Masashi

AU - Kijima, Shuji

AU - Uno, Takeaki

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

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U2 - 10.1007/11917496_7

DO - 10.1007/11917496_7

M3 - Conference contribution

AN - SCOPUS:33845535886

SN - 3540483810

SN - 9783540483816

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 68

EP - 77

BT - Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers

PB - Springer Verlag

T2 - 32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006

Y2 - 22 June 2006 through 24 June 2006

ER -