文章基本信息

标题：Reachability and Matching in Single Crossing Minor Free Graphs
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作者：Datta, Samir ; Gupta, Chetan ; Jain, Rahul 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：213
DOI：10.4230/LIPIcs.FSTTCS.2021.16
语种：English
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We show that for each single crossing graph H, a polynomially bounded weight function for all H-minor free graphs G can be constructed in logspace such that it gives nonzero weights to all the cycles in G. This class of graphs subsumes almost all classes of graphs for which such a weight function is known to be constructed in logspace. As a consequence, we obtain that for the class of H-minor free graphs where H is a single crossing graph, reachability can be solved in UL, and bipartite maximum matching can be solved in SPL, which are small subclasses of the parallel complexity class NC. In the restrictive case of bipartite graphs, our maximum matching result improves upon the recent result of Eppstein and Vazirani [David Eppstein and Vijay V. Vazirani, 2021], where they show an NC bound for constructing perfect matching in general single crossing minor free graphs.
关键词：Reachability;Matching;Logspace;Single-crossing minor free graphs