Thin strip graphs

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)203-210
Number of pages8
JournalDiscrete Applied Mathematics
Volume216
DOIs
Publication statusPublished - Jan 10 2017
Externally publishedYes

Fingerprint

Strip
Graph in graph theory
Interval Graphs
Unit Disk
Comparability Graph
Unit Disk Graph
Unit
Class
Line

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Hayashi, T., Kawamura, A., Otachi, Y., Shinohara, H., & Yamazaki, K. (2017). Thin strip graphs. 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.

In: Discrete Applied Mathematics, Vol. 216, 10.01.2017, p. 203-210.

Research output: Contribution to journalArticle

Hayashi, T, Kawamura, A, Otachi, Y, Shinohara, H & Yamazaki, K 2017, 'Thin strip graphs', Discrete Applied Mathematics, vol. 216, pp. 203-210. https://doi.org/10.1016/j.dam.2015.01.018
Hayashi T, Kawamura A, Otachi Y, Shinohara H, Yamazaki K. Thin strip graphs. Discrete Applied Mathematics. 2017 Jan 10;216:203-210. https://doi.org/10.1016/j.dam.2015.01.018
Hayashi, Takashi ; Kawamura, Akitoshi ; Otachi, Yota ; Shinohara, Hidehiro ; Yamazaki, Koichi. / Thin strip graphs. In: Discrete Applied Mathematics. 2017 ; Vol. 216. pp. 203-210.
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