Graph Bipartization Problem with Applications to Via Minimization in VLSI Design

Abstract

The bipartization problem for a graph [Formula: see text] asks for finding a subset [Formula: see text] of [Formula: see text] such that the induced subgraph [Formula: see text] is bipartite and [Formula: see text] is maximized. This problem has significant applications in the via minimization of VLSI design. The problem has been proved NP-complete and the fixed parameter solvability has been known in the literature. This paper presents several polynomial-time algorithms for special graph families, such as split graphs, co-bipartite graphs, chordal graphs, and permutation graphs.