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- W4288365770 abstract "In the {sc Cluster Deletion} problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of {sc Cluster Deletion} is NP-complete on ($P_5$-free) chordal graphs, whereas {sc Cluster Deletion} is solved in polynomial time on split graphs. However, the existence of a polynomial-time algorithm of {sc Cluster Deletion} on interval graphs, a proper subclass of chordal graphs, remained a well-known open problem. Our main contribution is that we settle this problem in the affirmative, by providing a polynomial-time algorithm for {sc Cluster Deletion} on interval graphs. Moreover, despite the simple formulation of the algorithm on split graphs, we show that {sc Cluster Deletion} remains NP-complete on a natural and slight generalization of split graphs that constitutes a proper subclass of $P_5$-free chordal graphs. To complement our results, we provide two polynomial-time algorithms for {sc Cluster Deletion} on subclasses of such generalizations of split graphs." @default.
- W4288365770 created "2022-07-29" @default.
- W4288365770 creator A5031344191 @default.
- W4288365770 creator A5050290231 @default.
- W4288365770 date "2019-04-20" @default.
- W4288365770 modified "2023-09-25" @default.
- W4288365770 title "Cluster Deletion on Interval Graphs and Split Related Graphs" @default.
- W4288365770 doi "https://doi.org/10.48550/arxiv.1904.09470" @default.
- W4288365770 hasPublicationYear "2019" @default.
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