The Simple Reachability Problem in Switch Graphs

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Abstract

Switch graphs as introduced in [Coo03] are a natural generalization of graphs where edges are interpreted as train tracks connecting switches: Each switch has an obligatory incident edge which has to be used by every path going through this switch. We prove that the simple reachability problem in switch graphs is NP-complete in general, but we describe a polynomial time algorithm for the undirected case. As an application, this can be used to find an augmenting path for bigamist matchings and thus iteratively construct a maximum bigamist matching for a given bipartite graph with red and blue edges, that is the maximum set of vertex disjoint triples consisting of one bigamist vertex connected to two monogamist vertices with two different colors. This this gives an independent direct solution to an open problem in [SGYB05].