eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-07
50:1
50:12
10.4230/LIPIcs.ISAAC.2016.50
article
On the Complexity of Matching Cut in Graphs of Fixed Diameter
Le, Hoang-Oanh
Le, Van Bang
In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been proved that Matching Cut is polynomially solvable for graphs of diameter two. In this paper, we show that, for any fixed integer d geq 4, Matching Cut is NP-complete in the class of graphs of diameter d. This almost resolves an open problem posed by Borowiecki and Jesse-Józefczyk in [Matching cutsets in graphs of diameter 2, Theoretical Computer Science 407 (2008) 574-582].
We then show that, for any fixed integer d geq 5, Matching Cut is NP-complete even when restricted to the class of bipartite graphs of diameter d. Complementing the hardness results, we show that Matching Cut is in polynomial-time solvable in the class of bipartite graphs of diameter at most three, and point out a new and simple polynomial-time algorithm solving Matching Cut in graphs of diameter 2.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol064-isaac2016/LIPIcs.ISAAC.2016.50/LIPIcs.ISAAC.2016.50.pdf
matching cut
NP-hardness
graph algorithm
computational complexity
decomposable graph