On approximating transitivity and tractability of graphs
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In the general case, in a simple, undirected graph, the problems of finding the largest clique, minimum colouring, maximum independent set and minimum vertex cover are NP-hard. But, there exists some families of graphs, called perfect graphs, where these problems become tractable. One particular class of perfect graphs are the the underlying undirected graphs of transitive digraphs- called comparability graphs. We define a new parameter β to approximate the intransitivity of a given graph. We also use β to give a measure of complexity of finding the largest clique. As β gets worse, the ...