Geodesic
Homomorphisms of edge-colored graphs and Coxeter groups
Journal of Algebraic Combinatorics, Tome 8 (1998) no. 1, pp. 5-13.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G _{1} = ( V _{1} , E _{1} )and G _2 = ( V _2 , E _2 )$ G_1 = (V_1 ,E_1 )text and G_2 = (V_2 ,E_2 ) be two edge-colored graphs (without multiple edges or loops). A $homomorphism$ is a mapping $ V _{1} \textregistered V _{2}$ V_1 $\mapsto V$_2 for which, for every pair of adjacent vertices $u$ and $v$ of $G _{1}, \varphi( u)$ and $\varphi$(v) are adjacent in $G _{2}$ and the color of the edge $\varphi$(u) $\varphi$(v) is the same as that of the edge $uv$. We prove a number of results asserting the existence of a graph $G$ , edge-colored from a set $C$, into which every member from a given class of graphs, also edge-colored from $C$, maps homomorphically.
Keywords: graph, homomorphism, Coxeter group, reflection group 
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     author = {Alon, N. and Marshall, T.H.},
     title = {Homomorphisms of edge-colored graphs and {Coxeter} groups},
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Alon, N.; Marshall, T.H. Homomorphisms of edge-colored graphs and Coxeter groups. Journal of Algebraic Combinatorics, Tome 8 (1998) no. 1, pp. 5-13. http://geodesic.mathdoc.fr/item/JAC_1998__8_1_a4/