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Since interval graphs are circular-arc graphs, we also obtain a linear time algorithm on interval graphs.

This problem is solved for unit interval graphs.

We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O k9n) time.

Interval graphs play important roles in analysis of DNA chains in Benzer [S.

We also give O(√nlogn -approximation for the problem on general weighted interval graphs.

[6] and Soulignac [9] present a proof that the class of proper interval graphs precisely the class of unit interval graphs.

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Similar(20)

LetGbe an unit interval graph.

LetGbe a connected unit interval graph.

Thereby favorable characteristics with regard to coloring, the interval graph properties, get lost.

We show an example of an unit interval graph G in Fig. 1.

Fig. 1 Algorithm CPP returns the 2-power of path P6=v1,v2,v3,0,v4,v5 for unit interval graph G.

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