On the interval number of special graphs

نویسندگان

  • József Balogh
  • Pascal Ochem
  • András Pluhár
چکیده

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) d12(d þ 1)e. 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

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عنوان ژورنال:
  • Journal of Graph Theory

دوره 46  شماره 

صفحات  -

تاریخ انتشار 2004