A simple linear-time algorithm to recognize interval graphs
The fastest known algorithm for recognizing interval graphs  iteratively manipulates the system of all maximal cliques of the given graph in a rather complicated way in order to construct a consecutive arrangement (more precisely: a tree representation of all possible such consecutive arrangements). We present a much simpler algorithm which uses a related, but much more informative tree representation of interval graphs. This tree is constructed in an on-line fashion by adding vertices to the graph in a predefined order such that adding a vertex u takes O(|Adj(u)|) amortized time.
Key wordsinterval graphs on-line recognition graph algorithm perfect elimination scheme modified PQ-tree
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