Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

[Show abstract] [Hide abstract]
ABSTRACT: We introduce a class of digraphs analogous to proper interval graphs and bigraphs. They are defined via a geometric representation by two inclusionfree 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 socalled MinMax orderings, and the existence of certain graph polymorphisms. MinMax orderings arose in the study of minimum cost homomorphism problems: if $H$ admits a a MinMax ordering (or a certain extension of MinMax 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 MinMax ordering; we also similarly characterize digraphs with an extended MinMax ordering. In a companion paper, we shall apply this latter characterization to derive a conjectured dichotomy classification for the minimum cost homomorphism problemsnamely, we shall prove that the minimum cost homomorphism problem to a digraph that does not admit an extended MinMax ordering is NPcomplete. SIAM Journal on Discrete Mathematics 01/2012; 26(4):15761596. DOI:10.1137/100783844 · 0.58 Impact Factor

[Show abstract] [Hide abstract]
ABSTRACT: The minimum cost homomorphism problem has arisen as a natural and useful optimization problem in the study of graph (and digraph) coloring and homomorphisms: it unifies a number of other well studied optimization problems. It was shown by Gutin, Rafiey, and Yeo that the minimum cost problem for homomorphisms to a digraph $H$ that admits a socalled extended MinMax ordering is polynomial time solvable, and these authors conjectured that for all other digraphs $H$ the problem is NPcomplete. In a companion paper, we gave a forbidden structure characterization of digraphs that admit extended MinMax orderings. In this paper, we apply this characterization to prove Gutin's conjecture. SIAM Journal on Discrete Mathematics 01/2012; 26(4):1597–1608. DOI:10.1137/100783856 · 0.58 Impact Factor