文章基本信息

标题：The Complexity of Finding Fair Independent Sets in Cycles
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作者：Ishay Haviv
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：185
页码：4:1-4:14
DOI：10.4230/LIPIcs.ITCS.2021.4
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Let G be a cycle graph and let Vâ,,â¦,V_m be a partition of its vertex set into m sets. An independent set S of G is said to fairly represent the partition if S â^© V_i â¥ 1/2â<. V_i - 1 for all i â^^ [m]. It is known that for every cycle and every partition of its vertex set, there exists an independent set that fairly represents the partition (Aharoni et al., A Journey through Discrete Math., 2017). We prove that the problem of finding such an independent set is PPA-complete. As an application, we show that the problem of finding a monochromatic edge in a Schrijver graph, given a succinct representation of a coloring that uses fewer colors than its chromatic number, is PPA-complete as well. The work is motivated by the computational aspects of the "cycle plus triangles" problem and of its extensions.
关键词：Fair independent sets in cycles; the complexity class {PPA}; Schrijver graphs