### 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 language | English |
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Pages (from-to) | 309-318 |

Number of pages | 10 |

Journal | Graphs and Combinatorics |

Volume | 18 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 1 2002 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

*Graphs and Combinatorics*,

*18*(2), 309-318. https://doi.org/10.1007/s003730200023