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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1297,
author = {Juan Jos\'e Montellano-Ballesteros},
title = {An anti-Ramsey theorem on edge-cuts},
journal = {Discussiones Mathematicae Graph Theory},
volume = {26},
year = {2006},
pages = {19-21},
zbl = {1107.05037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1297}
}
Juan José Montellano-Ballesteros. An anti-Ramsey theorem on edge-cuts. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 19-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1297/
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