Abstract
Given a density measure Π, an undirected graph G and a nonnegative integer k, a Π-CLUSTER EDITING problem is to decide whether G can be modified into a graph where all connected components are Π-cliques, by at most k edge modifications. Previous studies have been conducted on the complexity and fixed-parameter tractability (FPT) of Π-CLUSTER EDITING based on several different density measures. However, whether these conclusions hold on bipartite graphs is yet to be examined. In this paper, we focus on three different density measures for bipartite graphs: (1) having at most s missing edges for each vertex (s-biplex), (2) having average degree at least |V| − s (average-s-biplex) and (3) having at most s missing edges within a single disjoint component (s-defective bicliques). First, the NP-completeness of the three problems is discussed and afterwards we show all these problems are fixed-parameter tractable with respect to the parameter (s,k).
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