On the hardness of problems around s-clubs on split graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-01-24 DOI:10.1016/j.dam.2025.01.023

Cristina Bazgan , Pinar Heggernes , André Nichterlein , Thomas Pontoizeau

引用次数: 0

Abstract

We investigate the complexity of problems related to

s

-clubs. Given a graph, an

s

-club is a subset of vertices such that the subgraph induced by it has diameter at most

s

. We show that partitioning a split graph into two 2-clubs is NP-hard. Moreover, we prove that finding the minimum number of edges to add to a split graph in order to obtain a diameter of at most 2 is W[2]-hard with respect to the number of edges to add. Finally we show that finding the minimum number of edges to keep within a split graph of diameter 2 or 3 in order to maintain its diameter is NP-complete.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.