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IWOCA 2011: Combinatorial Algorithms pp 135-143

# Complexity of Cycle Transverse Matching Problems

• Ross Churchley
• Jing Huang
• Xuding Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)

## Abstract

The stable transversal problem for a fixed graph H asks whether a graph contains a stable set that meets every induced copy of H in the graph. Stable transversal problems generalize several vertex partition problems and have been studied for various classes of graphs. Following a result of Farrugia, the stable transversal problem for each C with ℓ ≥ 3 is NP-complete. In this paper, we study an ‘edge version’ of these problems. Specifically, we investigate the problem of determining whether a graph contains a matching that meets every copy of H. We show that the problem for C 3 is polynomial and for each C with ℓ ≥ 4 is NP-complete. Our results imply that the stable transversal problem for each C with ℓ ≥ 4 remains NP-complete when it is restricted to line graphs. We show by contrast that the stable transversal problem for C 3, when restricted to line graphs, is polynomial.

## Keywords

Stable transversal problem transverse matching problem algorithm complexity

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2011

## Authors and Affiliations

• Ross Churchley
• 1
• Jing Huang
• 1
• Xuding Zhu
• 2
1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
2. 2.Department of mathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China

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