Abstract
Folding problems in graphs demand to find a pair of disjoint subsets X, Y of the vertex set such that | X|=;| Y|=; m, and there is no edge between X and Y, or the set of edges between X and Y is restricted in a certain way. The study of such problems is motivated by an application in VLSI layout, namely the minimization of physical area of programmable logic arrays (PLAs). Here we investigate the complexity of folding problems in a number of standard graph classes. We show the NP-completeness of BLOCK FOLDING (BF) and VARIABLE FOLDING (VF) for bipartite graphs and split graphs. Polynomial cases for BF (trapezoid, circular arc, and directed path graphs) are obtained by standard dynamic programming methods. Polynomial solutions of VF are given for cographs, trees and interval graphs.
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