Conflict-Free graph orientations with parity constraints

Authors:
Sarah Cannon;Mashhood Ishaque;Csaba D. Tóth
Affiliations:
Department of Mathematics, Tufts University, Medford, MA, USA,Department of Computer Science, Tufts University, Medford, MA;Department of Computer Science, Tufts University, Medford, MA;Department of Computer Science, Tufts University, Medford, MA, USA,Department of Mathematics and Statistics, University of Calgary, AB, Canada
Venue:
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Year:
2012

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Abstract

It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a multigraph G=(V,E): (1) an exact conflict constraint is an edge set C⊆E and a vertex v∈V such that C should not equal the set of incoming edges at v; (2) a subset conflict constraint is an edge set C⊆E and a vertex v∈V such that C should not be a subset of incoming edges at v. We show that it is NP-complete to decide whether G has an even orientation with exact or subset conflicts, for all conflict sets of size two or higher. We present efficient algorithms for computing parity constrained orientations with disjoint exact or subset conflict pairs.