A Maximum Cardinality Cut Algorithm for Co-bipartite and Split Graphs Using Bimodular Decomposition

Year 2021, Volume: 13 Issue: 1, 182 - 191, 30.06.2021

Arman Boyacı Mordechai Shalom

https://doi.org/10.47000/tjmcs.748563

Abstract

The maximum cardinality cut (MaxCut) problem remains NP-complete for co-bipartite graphs and
for split graphs. Based on modular decomposition, in [3] it is shown that MaxCut is polynomial-time solvable for graphs that are factorable to bounded treewidth graphs. However, this approach fails in co-bipartite graphs because the modules of a co-bipartite graph are exactly twins and connected components. In this work we extend the result of [3] to co-bipartite graphs using the concept of bimodules and bimodular decomposition proposed in [6]. Namely, we show thatMaxCut is polynomial-time solvable for co-bipartite graphs that can be factored to bounded treewidth graphs using bimodular decomposition.

Keywords

Maximum cardinality cut, bimodular decomposition, split graphs.

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