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Discussiones Mathematicae Graph Theory 26(1) (2006) 19-21
DOI: https://doi.org/10.7151/dmgt.1297

AN ANTI-RAMSEY THEOREM ON EDGE-CUTS

Juan José Montellano-Ballesteros

Instituto de Matemáticas, U.N.A.M.
Ciudad Universitaria, Coyoacán 04510
México, D.F. México
e-mail: juancho@math.unam.mx

Abstract

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.

2000 Mathematics Subject Classification: 05C15, 05C40.

References

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Received 18 September 2004
Revised 28 November 2005