Split and balanced colorings of complete graphs

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An (r,n)-split coloring of a complete graph is an edge coloring with r colors under which the vertex set is partitionable into r parts so that for each i, part i does not contain Kn in color i. This generalizes the notion of split graphs which correspond to (2, 2)-split colorings. The smallest N for which the complete graph KN has a coloring which is not (r,n)-split is denoted by fr(n). Balanced (r,n)-colorings are defined as edge r-colorings of KN such that every subset of ⌈N/r⌉ vertices contains a monochromatic Kn in all colors. Then gr(n) is defined as the smallest N such that KN has a balanced (r,n)-coloring. The definitions imply that fr(n)≤g,(n). The paper gives estimates and exact values of these functions for various choices of parameters.

Original languageEnglish
Pages (from-to)79-86
Number of pages8
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - Apr 6 1999



  • Balanced coloring
  • Split graphs
  • Vertex set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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