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Absolute Retracts and Varieties of Reflexive Graphs

Published online by Cambridge University Press:  20 November 2018

Pavol Hell  and
Ivan Rival
Pavol Hell
Affiliation:
Simon Fraser University, Burnaby, British Columbia
Ivan Rival
Affiliation:
The University of Ottawa, Ottawa, Ontario
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For a graph G, let V(G) denote its vertex set and E(G) its edge set. Here we shall only consider reflexive graphs, that is graphs in which every vertex is adjacent to itself. These adjacencies, i.e., the loops, will not be depicted in the figures, although we always assume them present. For graphs G and H, an edge-preserving map (or homomorphism) of G to H is a mapping of V(G) to V(H) such that f(g) is adjacent to f(g′) in H whenever g is adjacent to g′ in G. Because our graphs are reflexive, an edge-preserving map can identify adjacent vertices, i.e., possibly f(g) = f(g′) for some g adjacent to g′, cf. Figure 1(a).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 3 , 01 June 1987 , pp. 544 - 567
Copyright
Copyright © Canadian Mathematical Society 1987

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