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A Canonical Factorization for Graph Homomorphisms

Published online by Cambridge University Press:  20 November 2018

Barry Fawcett
Barry Fawcett*
Affiliation:
Laurentian University, Sudbury, Ontario
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The graphs are undirected, without loops or multiple edges. The edge set E(X) of a graph X is a set of certain unordered pairs [x, y] of distinct elements of the vertex set V(X). For x ϵ V(X) we denote by E(x; X) the edges of X incident with x. A (homo)morphism ϕ : X ⟶ Y is a function from V(X) to V(Y) which preserves edges; thus it induces ϕ# : E(X) ⟶ E(Y) by ϕ# [x, x’] = [ϕx, ϕx’].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 738 - 743
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Fawcett, B., A categorical characterization of the four colour theorem, submitted.Google Scholar
2. Hell, P., Retracts of graphs, Thesis, U. de Montréal, 1971.Google Scholar
3. Schubert, H., Categories (Academic Press, Berlin, 1972).Google Scholar