A finite basis characterization of α-split colorings

A. Gyárfás, André E. Kézdy, K. Jeno Lehel

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Fix t > 1, a positive integer, and a = (a1,...,at) a vector of nonnegative integers. A t-coloring of the edges of a complete graph is called a-split if there exists a partition of the vertices into t sets V1,...,Vt such that every set of ai + 1 vertices in Vi contains an edge of color i, for i = 1,...,t. We combine a theorem of Deza with Ramsey's theorem to prove that, for any fixed a, the family of a-split colorings is characterized by a finite list of forbidden induced subcolorings. A similar hypergraph version follows from our proofs. These results generalize previous work by Kézdy et al. (J. Combin. Theory Ser. A 73(2) (1996) 353) and Gyárfás (J. Combin. Theory Ser. A 81(2) (1998) 255). We also consider other notions of splitting.

Original languageEnglish
Pages (from-to)415-421
Number of pages7
JournalDiscrete Mathematics
Volume257
Issue number2-3
Publication statusPublished - Nov 28 2002

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Coloring
Colouring
Ramsey's Theorem
Integer
Hypergraph
Complete Graph
Non-negative
Partition
Color
Generalise
Theorem
Family

Keywords

  • Coloring
  • Finite basis
  • Ramsey theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Gyárfás, A., Kézdy, A. E., & Lehel, K. J. (2002). A finite basis characterization of α-split colorings. Discrete Mathematics, 257(2-3), 415-421.

A finite basis characterization of α-split colorings. / Gyárfás, A.; Kézdy, André E.; Lehel, K. Jeno.

In: Discrete Mathematics, Vol. 257, No. 2-3, 28.11.2002, p. 415-421.

Research output: Contribution to journalArticle

Gyárfás, A, Kézdy, AE & Lehel, KJ 2002, 'A finite basis characterization of α-split colorings', Discrete Mathematics, vol. 257, no. 2-3, pp. 415-421.
Gyárfás A, Kézdy AE, Lehel KJ. A finite basis characterization of α-split colorings. Discrete Mathematics. 2002 Nov 28;257(2-3):415-421.
Gyárfás, A. ; Kézdy, André E. ; Lehel, K. Jeno. / A finite basis characterization of α-split colorings. In: Discrete Mathematics. 2002 ; Vol. 257, No. 2-3. pp. 415-421.
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