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On homomorphisms to acyclic local tournaments

✍ Scribed by Pavol Hell; Huishan Zhou; Xuding Zhu

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 233 KB
Volume: 20
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190200410

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✦ Synopsis

Abstract

A homomorphism of a digraph to another digraph is an edgepreserving vertex mapping. A local tournament is a digraph in which the inset as well as the outset of each vertex induces a tournament. Thus acyclic local tournaments generalize both directed paths and transitive tournaments. In both these cases there is a simple characterization of homomorphic preimages. Namely, if H is a directed path, or a transitive tournament, then G admits a homomorphism to H if and only if each oriented path which admits a homomorphism to G also admits a homomorphism to H. We prove that this result holds for all acyclic local tournaments. © 1995 John Wiley & Sons, Inc.

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