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On the interval number of special graphs
Author(s) -
Balogh József,
Ochem Pascal,
Pluhár András
Publication year - 2004
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.20005
Subject(s) - combinatorics , mathematics , independence number , discrete mathematics , bipartite graph , graph , interval graph , line graph , pathwidth
The interval number of a graph G is the least natural number t such that G is the intersection graph of sets, each of which is the union of at most t intervals, denoted by i ( G ). Griggs and West showed that $i(G)\le \lceil {1\over 2} (d+1)\rceil $ . We describe the extremal graphs for that inequality when d is even. For three special perfect graph classes we give bounds on the interval number in terms of the independence number. Finally, we show that a graph needs to contain large complete bipartite induced subgraphs in order to have interval number larger than the random graph on the same number of vertices. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 241–253, 2004