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

2009/07/17 by Arash Rafiey, Pavol Hell, Rafiey, Arash +1
Computer Science · #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #cs.DM #cs.DS

paper · pdf · doi:10.48550/arxiv.0907.3016

arxiv created 2009/07/17 · arxiv updated 2009/12/01

Abstract

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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