Duality for Min-Max Orderings and Dichotomy for Min Cost Homomorphisms

Details Duality for Min-Max Orderings and Dichotomy for Min Cost Homomorphisms Duality for Min-Max Orderings and Dichotomy for Min Cost Homomorphisms

2009-07-17

arxiv.org/abs/0907.3016v1

Computer Science

Discrete Mathematics

Scientific paper

Min-Max orderings correspond to conservative lattice polymorphisms. Digraphs with Min-Max orderings have polynomial time solvable minimum cost homomorphism problems. They can also be viewed as digraph analogues of proper interval graphs and bigraphs. We give a forbidden structure characterization of digraphs with a Min-Max ordering which implies a polynomial time recognition algorithm. We also similarly characterize digraphs with an extended Min-Max ordering, and we apply this characterization to prove a conjectured form of dichotomy for minimum cost homomorphism problems.

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