TY - JOUR

T1 - Thin strip graphs

AU - Hayashi, Takashi

AU - Kawamura, Akitoshi

AU - Otachi, Yota

AU - Shinohara, Hidehiro

AU - Yamazaki, Koichi

N1 - Funding Information:
Partially supported by JSPS KAKENHI Grant Numbers 23240001, 24500007, 25730003 and MEXT KAKENHI Grant Numbers 24106002, 24106004.
Publisher Copyright:
© 2015 Elsevier B.V.

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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U2 - 10.1016/j.dam.2015.01.018

DO - 10.1016/j.dam.2015.01.018

M3 - Article

AN - SCOPUS:84921944953

SN - 0166-218X

VL - 216

SP - 203

EP - 210

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -