### Abstract

Let χ(G) and ω(G) denote the chromatic number and clique number of a graph G. We prove that _{χ} can be bounded by a function of ω for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line) satisfy χ≤2t(ω-1) for ω≥2. Overlap graphs satisfy χ≤2^{ω}ω^{2}(ω-1).

Original language | English |
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Pages (from-to) | 161-166 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 55 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**On the chromatic number of multiple interval graphs and overlap graphs.** / Gyárfás, A.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 55, no. 2, pp. 161-166. https://doi.org/10.1016/0012-365X(85)90044-5

}

TY - JOUR

T1 - On the chromatic number of multiple interval graphs and overlap graphs

AU - Gyárfás, A.

PY - 1985

Y1 - 1985

N2 - Let χ(G) and ω(G) denote the chromatic number and clique number of a graph G. We prove that χ can be bounded by a function of ω for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line) satisfy χ≤2t(ω-1) for ω≥2. Overlap graphs satisfy χ≤2ωω2(ω-1).

AB - Let χ(G) and ω(G) denote the chromatic number and clique number of a graph G. We prove that χ can be bounded by a function of ω for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line) satisfy χ≤2t(ω-1) for ω≥2. Overlap graphs satisfy χ≤2ωω2(ω-1).

UR - http://www.scopus.com/inward/record.url?scp=0010757331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010757331&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(85)90044-5

DO - 10.1016/0012-365X(85)90044-5

M3 - Article

AN - SCOPUS:0010757331

VL - 55

SP - 161

EP - 166

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -