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# Finding paths in graphs avoiding forbidden transitions.

Szeider, S. (2003) 'Finding paths in graphs avoiding forbidden transitions.', Discrete applied mathematics., 126 (2-3). pp. 261-273.

## Abstract

Let v be a vertex of a graph G; a transition graph T(v) of v is a graph whose vertices are the edges incident with v. We consider graphs G with prescribed transition systems T={T(v) | vV(G)}. A path P in G is called T-compatible, if each pair uv,vw of consecutive edges of P form an edge in T(v). Let be a given class of graphs (closed under isomorphism). We study the computational complexity of finding T-compatible paths between two given vertices of a graph for a specified transition system . Our main result is that a dichotomy holds (subject to the assumption P≠NP). That is, for a considered class , the problem is either (1) NP-complete, or (2) it can be solved in linear time. We give a criterion—based on vertex induced subgraphs—which decides whether (1) or (2) holds for any given class.

Item Type: Article Compatible path, Transition, Edge-colored graph, Forbidden pairs, NP-Completeness, Linear time algorithm. PDF - Accepted Version (136Kb) Peer-reviewed http://dx.doi.org/10.1016/S0166-218X(02)00251-2 14 Oct 2008 10 Aug 2011 16:32

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