FUN 2012: Fun with Algorithms pp 57-68

# Conflict-Free Graph Orientations with Parity Constraints

• Sarah Cannon
• Mashhood Ishaque
• Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)

## 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.

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## Authors and Affiliations

• Sarah Cannon
• 1
• 2
• Mashhood Ishaque
• 2
• Csaba D. Tóth
• 2
• 3
1. 1.Department of MathematicsTufts UniversityMedfordUSA
2. 2.Department of Computer ScienceTufts UniversityMedfordUSA
3. 3.Department of Mathematics and StatisticsUniversity of CalgaryCanada