Vertex colouring edge partitions

  • Authors:

  • L. Addario-Berry;R. E. L. Aldred;K. Dalal;B. A. Reed

  • Affiliations:

  • School of Computer Science, McGill University, University St., Montreal, QC, H3A 2A7, Canada;Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin, New Zealand;School of Computer Science, McGill University, University St., Montreal, QC, H3A 2A7, Canada;School of Computer Science, McGill University, University St., Montreal, QC, H3A 2A7, Canada

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2005

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Abstract

A partition of the edges of a graph G into sets {S1,..., Sk} defines a multiset Xv for each vertex v where the multiplicity of i in Xv is the number of edges incident to v in Si We show that the edges of every graph can be partitioned into 4 sets such that the resultant multisets give a vertex colouring of G. In other words, for every edge (u, v) of G, Xu ≠ Xv. Furthermore, if G has minimum degree at least 1000, then there is a partition of E(G) into 3 sets such that the corresponding multisets yield a vertex colouring.