### Abstract

A unit disk graph is a c-strip graph if it has a unit disk representation in which all centers of the unit disks lie between two parallel lines at distance c. The classes of c-strip graphs for various c are studied in the literature. For example, the 0-strip graphs are exactly the unit interval graphs, and every 3/2-strip graph is a co-comparability graph. In this paper, we introduce the class of thin strip graphs and study their properties. A graph is a thin strip graph if it is a c-strip graph for every c>0. We show that there is no constant t such that the t-strip graphs are exactly the thin strip graphs. We also show that the class of thin strip graphs properly includes the class of mixed unit interval graphs.

Original language | English |
---|---|

Pages (from-to) | 203-210 |

Number of pages | 8 |

Journal | Discrete Applied Mathematics |

Volume | 216 |

DOIs | |

Publication status | Published - Jan 10 2017 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*216*, 203-210. https://doi.org/10.1016/j.dam.2015.01.018

**Thin strip graphs.** / Hayashi, Takashi; Kawamura, Akitoshi; Otachi, Yota; Shinohara, Hidehiro; Yamazaki, Koichi.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 216, pp. 203-210. https://doi.org/10.1016/j.dam.2015.01.018

}

TY - JOUR

T1 - Thin strip graphs

AU - Hayashi, Takashi

AU - Kawamura, Akitoshi

AU - Otachi, Yota

AU - Shinohara, Hidehiro

AU - Yamazaki, Koichi

PY - 2017/1/10

Y1 - 2017/1/10

N2 - A unit disk graph is a c-strip graph if it has a unit disk representation in which all centers of the unit disks lie between two parallel lines at distance c. The classes of c-strip graphs for various c are studied in the literature. For example, the 0-strip graphs are exactly the unit interval graphs, and every 3/2-strip graph is a co-comparability graph. In this paper, we introduce the class of thin strip graphs and study their properties. A graph is a thin strip graph if it is a c-strip graph for every c>0. We show that there is no constant t such that the t-strip graphs are exactly the thin strip graphs. We also show that the class of thin strip graphs properly includes the class of mixed unit interval graphs.

AB - A unit disk graph is a c-strip graph if it has a unit disk representation in which all centers of the unit disks lie between two parallel lines at distance c. The classes of c-strip graphs for various c are studied in the literature. For example, the 0-strip graphs are exactly the unit interval graphs, and every 3/2-strip graph is a co-comparability graph. In this paper, we introduce the class of thin strip graphs and study their properties. A graph is a thin strip graph if it is a c-strip graph for every c>0. We show that there is no constant t such that the t-strip graphs are exactly the thin strip graphs. We also show that the class of thin strip graphs properly includes the class of mixed unit interval graphs.

UR - http://www.scopus.com/inward/record.url?scp=84921944953&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921944953&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2015.01.018

DO - 10.1016/j.dam.2015.01.018

M3 - Article

AN - SCOPUS:84921944953

VL - 216

SP - 203

EP - 210

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -