On Structural Parameterizations of the Matching Cut Problem

N R, Aravind and Kalyanasundaram, Subrahmanyam and Kare, A S (2017) On Structural Parameterizations of the Matching Cut Problem. In: International Conference on Combinatorial Optimization and Applications, December 16-18, 2017, China.

Full text not available from this repository. (Request a copy)

Abstract

In an undirected graph, a matching cut is a partition of vertices into two sets such that the edges across the sets induce a matching. The matching cut problem is the problem of deciding whether a given graph has a matching cut. The matching cut problem can be expressed using a monadic second-order logic (MSOL) formula and hence is solvable in linear time for graphs with bounded tree-width. However, this approach leads to a running time of f(ϕ,t)nO(1), where ϕ is the length of the MSOL formula, t is the tree-width of the graph and n is the number of vertices of the graph. In [Theoretical Computer Science, 2016], Kratsch and Le asked to give a single exponential algorithm for the matching cut problem with tree-width alone as the parameter. We answer this question by giving a 2O(t)nO(1) time algorithm. We also show the tractability of the matching cut problem when parameterized by neighborhood diversity and other structural parameters.

[error in script]

IITH Creators: