The chromatic spectrum of mixed hypergraphs

Tao Jiang, Dhruv Mubayi, Zsolt Tuza, Vitaly Voloshin, Douglas B. West

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

A mixed hypergraph is a triple ℋ = (X, script C sign, D), where X is the vertex set, and each of script C sign, D is a list of subsets of X. A strict k-coloring of ℋ is a surjection c: X → {1,...,k} such that each member of script C sign has two vertices assigned a common value and each member of D has two vertices assigned distinct values. The feasible set of H is {k: H has a strict A-coloring}. Among other results, we prove that a finite set of positive integers is the feasible set of some mixed hypergraph if and only if it omits the number 1 or is an interval starting with 1. For the set {s, t} with 2 ≤ s ≤ t - 2, the smallest realization has 2t - s vertices. When every member of script C sign ∪ D is a single interval in an underlying linear order on the vertices, the feasible set is also a single interval of integers.

Original languageEnglish
Pages (from-to)309-318
Number of pages10
JournalGraphs and Combinatorics
Volume18
Issue number2
DOIs
Publication statusPublished - Dec 1 2002

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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    Jiang, T., Mubayi, D., Tuza, Z., Voloshin, V., & West, D. B. (2002). The chromatic spectrum of mixed hypergraphs. Graphs and Combinatorics, 18(2), 309-318. https://doi.org/10.1007/s003730200023