The complexity of the matching-cut problem for planar graphs and other graph classes

Bonsma, Paul (2009) The complexity of the matching-cut problem for planar graphs and other graph classes. Journal of Graph Theory, 62 (2). pp. 109-126. ISSN 0364-9024

PDF
Restricted to UT campus only: Request a copy
234Kb

Abstract:	The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it is shown that the problem remains -complete for planar graphs with maximum degree four, answering a question by Patrignani and Pizzonia. It is also shown that the problem is -complete for planar graphs with girth five. The reduction is from planar graph 3-colorability and differs from earlier reductions. In addition, for certain graph classes polynomial time algorithms to find matching-cuts are described. These classes include claw-free graphs, co-graphs, and graphs with fixed bounded tree-width or clique-width.
Item Type:	Article
Copyright:	© 2009 Wiley
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/72723
Official URL:	http://dx.doi.org/10.1002/jgt.20390
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page

Metis ID: 214382