Abstract
A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A, B, C, D such that there are all possible edges between A and B, and no edges between C and D. We present a polynomial-time algorithm for testing whether a graph admits a skew partition. Our algorithm solves the more general list skew partition problem, where the input contains, for each vertex, a list containing some of the labels A, B, C, D of the four parts. Our polynomial-time algorithm settles the complexity of the original partition problem proposed by Chvátal, and answers a recent question of Feder, Hell, Klein and Motwani.
Research partially supported by CNPq, MCT/FINEP PRONEX Project 107/97, CAPES(Brazil)/COFECUB(France) Project 213/97, FAPERJ, and by FAPESP Proc. 96/04505-2.
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de Figueiredo, C.M.H., Klein, S., Kohayakawa, Y., Reed, B.A. (2000). Finding Skew Partitions Efficiently. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_18
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DOI: https://doi.org/10.1007/10719839_18
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