Canonical edge-colourings of locally finite graphs

Abstract

A variety of results on edge-colourings are proved, the main one being the following: ifG is a graph without loops or multiple edges and with maximum degree Δ=Δ(G), and if ν is a given integer 1≦ν≦Δ(G), thenG can be given a proper edge-colouring with the coloursc 1, ...,c Δ+1 with the additional property that any edge colouredc μ with μ≧ν is on a vertex which has on it edges coloured with at least ν − 1 ofc 1, ...,c v .

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Hilton, A.J.W. Canonical edge-colourings of locally finite graphs. Combinatorica 2, 37–51 (1982). https://doi.org/10.1007/BF02579280

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AMS subject classification (1980)

  • 05 C 15