Extended skew partition problem

A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A 1 , A 2 , B 1 , B 2 such that there are all possible edges between A 1 and A 2 , and no edges between B 1 and B 2 . We introduce the concept of ( n 1 , n 2 ) -extended skew partition which i...

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Bibliographic Details
Published in:	Discrete mathematics Vol. 306; no. 19; pp. 2438 - 2449
Main Authors:	Dantas, Simone, de Figueiredo, Celina M.H., Gravier, Sylvain, Klein, Sulamita
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 06.10.2006
Subjects:	2-SAT Algorithms and data structures Computational and structural complexity Skew partition Algorithms and data structures Skew partition Computational and structural complexity 2-SAT
ISSN:	0012-365X, 1872-681X
Online Access:	Get full text
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Summary:	A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A 1 , A 2 , B 1 , B 2 such that there are all possible edges between A 1 and A 2 , and no edges between B 1 and B 2 . We introduce the concept of ( n 1 , n 2 ) -extended skew partition which includes all partitioning problems into n 1 + n 2 nonempty parts A 1 , … , A n 1 , B 1 , … , B n 2 such that there are all possible edges between the A i parts, no edges between the B j parts, i ∈ { 1 , … , n 1 } , j ∈ { 1 , … , n 2 } , which generalizes the skew partition. We present a polynomial-time algorithm for testing whether a graph admits an ( n 1 , n 2 ) -extended skew partition. As a tool to complete this task we also develop a generalized 2-SAT algorithm, which by itself may have application to other partition problems.
ISSN:	0012-365X 1872-681X
DOI:	10.1016/j.disc.2005.12.034