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Martin Charles Golumbic,Michal Stern,Gila Morgenst

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Account on Intervalsclass of graphs are well understood, some old problems are still open. One such problem is the so-called interval count problem, which asks for the minimum number of different interval lengths needed to represent a given interval graph. Whereas graphs of interval count 1 coincide with unit interval

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Minimum Weighted Clique Cover on Strip-Composed Perfect Graphsdates back to 1984. More recently, Chudnovsky and Seymour [3] introduced a composition operation, strip-composition, in order to define their structural results for claw-free graphs; however, this composition operation is general and applies to non-claw-free graphs as well. In this paper, we show th

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Optimization Problems in Dotted Interval Graphsus classical graph-theoretic optimization problems in .-DI graphs of arbitrarily, but fixed, ...We show that ., ., and . can be solved in polynomial time in this graph class, answering an open question posed by Jiang .. We also show that . can be approximated within a factor of (1 + .) for any . > 0

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The Maximum Clique Problem in Multiple Interval Graphs (Extended Abstract)ne. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple interval graphs. The MAXIMUM CLIQUE problem, or the problem of finding the size of the maximum clique, is known to be NP-complete for .-interval graphs when . ≥ 3 and polynomial-time solvable when . = 1. The pro

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