Abstract | ||
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We introduce a class of digraphs analogous to proper interval graphs and bigraphs. They are defined via a geometric representation by two inclusion-free families of intervals satisfying a certain monotonicity condition; hence we call them monotone proper interval digraphs. They admit a number of equivalent definitions, including an ordering characterization by so-called Min-Max orderings, and the existence of certain graph polymorphisms. Min-Max orderings arose in the study of minimum cost homomorphism problems: if H admits a a Min-Max ordering (or a certain extension of Min-Max orderings), then the minimum cost homomorphism problem to H is known to admit a polynomial time algorithm. We give a forbidden structure characterization of monotone proper interval digraphs, which implies a polynomial time recognition algorithm. This characterizes digraphs with a Min-Max ordering; we also similarly characterize digraphs with an extended Min-Max ordering. In a companion paper, we shall apply this latter characterization to derive a conjectured dichotomy classification for the minimum cost homomorphism problems-namely, we shall prove that the minimum cost homomorphism problem to a digraph that does not admit an extended Min-Max ordering is NP-complete. |
Year | DOI | Venue |
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2012 | 10.1137/100783844 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | Field | DocType |
interval digraphs,Min-Max orderings,forbidden structure characterizations,minimum cost homomorphisms | Monotonic function,Discrete mathematics,Graph,Bigraph,Combinatorics,Geometric representation,Homomorphism,Recognition algorithm,Time complexity,Monotone polygon,Mathematics | Journal |
Volume | Issue | ISSN |
26 | 4 | 0895-4801 |
Citations | PageRank | References |
2 | 0.36 | 0 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
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Pavol Hell | 1 | 2638 | 288.75 |
Arash Rafiey | 2 | 339 | 28.08 |