Vertex-Colouring Edge-Weightings

A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted c v , is \( {\sum\nolimits_{e \mathrel\backepsilon v} {w{\left( e \right)}} } \). We show that the edges of every graph that does not contain a component isomorphic to K2 can be weighted from the set {1, . . . ,30} such that in the resulting vertex-colouring of G, for every edge (u,v) of G, c u c v .

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Correspondence to Louigi Addario-Berry.

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Addario-Berry, L., Dalal, K., McDiarmid, C. et al. Vertex-Colouring Edge-Weightings. Combinatorica 27, 1–12 (2007). https://doi.org/10.1007/s00493-007-0041-6

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Mathematics Subject Classification (2000):

  • 05C15