Geodesic
An anti-Ramsey theorem on edge-cuts
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 19-21

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Let G = (V(G), E(G)) be a connected multigraph and let h(G) be the minimum integer k such that for every edge-colouring of G, using exactly k colours, there is at least one edge-cut of G all of whose edges receive different colours. In this note it is proved that if G has at least 2 vertices and has no bridges, then h(G) = |E(G)| -|V(G)| + 2.
Keywords: anti-Ramsey, totally multicoloured, edge-cuts 
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Montellano-Ballesteros, Juan. An anti-Ramsey theorem on edge-cuts. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 19-21. http://geodesic.mathdoc.fr/item/DMGT_2006_26_1_a1/