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GRAPHS WITH FORBIDDEN HOMOMORPHIC IMAGES (1979)

Hell, P. ; Miller, D. J.

Oxford, UK : Blackwell Publishing Ltd

Annals of the New York Academy of Sciences 319 (1979), S. 0

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ISSN: 1749-6632

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Natural Sciences in General

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1749-6632.1979.tb32801.x

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Homomorphisms of graphs and of their orientations (1978)

Hell, P. ; Nešetřil, J.

Springer

Monatshefte für Mathematik 85 (1978), S. 39-48

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ISSN: 1436-5081

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Consider a set of graphs and all the homomorphisms among them. Change each graph into a digraph by assigning directions to its edges. Some of the homomorphisms preserve the directions and so remain as homomorphisms of the set of digraphs; others do not. We study the relationship between the original set of graph-homomorphisms and the resulting set of digraph-homomorphisms and prove that they are in a certain sense independent. This independence result no longer holds if we start with a proper class of graphs, or if we require that only one direction be given to each edge (unless each homomorphism is invertible, in which case we again prove independence). We also specialize the results to the set consisting of one graph and prove the independence of monoids (groups) of a graph and the corresponding digraph.