We analyse properties of geometric intersection graphs to show the strict containment between some natural classes of geometric intersection graphs. In particular, we show the following properties:A graph $G$ is outerplanar if and only if the 1-subdivision of $G$ is outer-segment.For each integer $k\ge 1$, the class of intersection graphs of segments with $k$ different lengths is a strict subclass of the class of intersection graphs of segments with $k+1$ different lengths.For each integer $k\ge 1$, the class of intersection graphs of disks with $k$ different sizes is a strict subclass of the class of intersection graphs of disks with $k+1$ different sizes.The class of outer-segment graphs is a strict subclass of the class of outer-string graphs.
@article{10_37236_6040,
author = {Sergio Cabello and Miha Jej\v{c}i\v{c}},
title = {Refining the hierarchies of classes of geometric intersection graphs},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6040},
zbl = {1355.05092},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6040/}
}
TY - JOUR
AU - Sergio Cabello
AU - Miha Jejčič
TI - Refining the hierarchies of classes of geometric intersection graphs
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6040/
DO - 10.37236/6040
ID - 10_37236_6040
ER -
%0 Journal Article
%A Sergio Cabello
%A Miha Jejčič
%T Refining the hierarchies of classes of geometric intersection graphs
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6040/
%R 10.37236/6040
%F 10_37236_6040
Sergio Cabello; Miha Jejčič. Refining the hierarchies of classes of geometric intersection graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6040
