A simple test for interval graphs
Interval graphs are a special class of chordal graphs. Several linear time algorithms have been designed to recognize interval graphs. All of these algorithms rely on the following fact: a graph is an interval graph iff there exists a linear order of its maximal cliques such that for each vertex v, all maximal cliques containing v are consecutive. We give a much simpler recogntion algorithm in this paper which directly place the intervals without even using maximal cliques. The key is to find a good ordering of intervals to be placed. An on-line version of the algorithm that takes O(mα(n)) time will be discussed in a separate paper.
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