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List Partitions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Motwani, Rajeev Klein, Sulamita Hell, Pavol Feder., Tomas
Copyright Year	2003
Abstract	List partitions generalize list colorings and list homomorphisms. (We argue that they may be called list "semihomomorphisms.") Each symmetric matrix M over 0,1,* defines a list partition problem. Different choices of the matrix M lead to many well-known graph theoretic problems, often related to graph perfection, including the problem of recognizing split graphs, finding homogeneous sets, clique cutsets, stable cutsets, and so on. The recent proof of the strong perfect graph theorem employs three kinds of decompositions that can be viewed as list partitions. We develop tools which allow us to classify the complexity of many list partition problems and, in particular, yield the complete classification for small matrices M. Along the way, we obtain a variety of specific results, including generalizations of Lovsz's communication bound on the number of clique-versus-stable-set separators, polynomial time algorithms to recognize generalized split graphs, a polynomial algorithm for the list version of the clique cutset problem, and the first subexponential algorithm for the skew cutset problem of Chvtal. We also show that the dichotomy (NP-complete versus polynomial time solvable), conjectured for certain graph homomorphism problems, would, if true, imply a slightly weaker dichotomy (NP-complete versus quasi-polynomial) for our list partition problems.
Starting Page	449
Ending Page	478
Page Count	30
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480100384055
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	quasi-polynomial algorithms split graphs 2-joins dichotomy skew cutsets communication bound Perfect graphs clique cutsets Coloring of graphs and hypergraphs constraint satisfaction problems Analysis of algorithms and problem complexity perfect graphs polynomial time algorithms NP-completeness graph partitions H-colorings Graph algorithms list homomorphisms
Content Type	Text
Resource Type	Article
Subject	Mathematics

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