Thin strip graphs

Takashi Hayashi; Akitoshi Kawamura; Yota Otachi; Hidehiro Shinohara; Koichi Yamazaki

doi:10.1016/j.dam.2015.01.018

Thin strip graphs

Takashi Hayashi, Akitoshi Kawamura, Yota Otachi, Hidehiro Shinohara, Koichi Yamazaki

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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	https://doi.org/10.1016/j.dam.2015.01.018
Publication status	Published - Jan 10 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2015.01.018

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title = "Thin strip graphs",

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.",

author = "Takashi Hayashi and Akitoshi Kawamura and Yota Otachi and Hidehiro Shinohara and Koichi Yamazaki",

note = "Funding Information: Partially supported by JSPS KAKENHI Grant Numbers 23240001, 24500007, 25730003 and MEXT KAKENHI Grant Numbers 24106002, 24106004. Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

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doi = "10.1016/j.dam.2015.01.018",

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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.

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EP - 210

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Thin strip graphs

Abstract

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