Circular Separation Dimension of a Subclass of Planar Graphs
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3
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A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering. The circular separation dimension of a graph $G$, denoted by $\pi^\circ(G)$, is the minimum number of circular orderings of the vertices of $G$ such that every pair of non-adjacent edges is separated in at least one of the circular orderings. This notion is introduced by Loeb and West in their recent paper. In this article, we consider two subclasses of planar graphs, namely $2$-outerplanar graphs and series-parallel graphs. A $2$-outerplanar graph has a planar embedding such that the subgraph obtained by removal of the vertices of the exterior face is outerplanar. We prove that if $G$ is $2$-outerplanar then $\pi^\circ(G) = 2$. We also prove that if $G$ is a series-parallel graph then $\pi^\circ(G) \leq 2$.
@article{DMTCS_2017_19_3_a9,
author = {Bharathi, Arpitha P. and De, Minati and Lahiri, Abhiruk},
title = {Circular {Separation} {Dimension} of a {Subclass} of {Planar} {Graphs}},
journal = {Discrete mathematics & theoretical computer science},
publisher = {mathdoc},
volume = {19},
number = {3},
year = {2017-2018},
doi = {10.23638/DMTCS-19-3-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-8/}
}
TY - JOUR AU - Bharathi, Arpitha P. AU - De, Minati AU - Lahiri, Abhiruk TI - Circular Separation Dimension of a Subclass of Planar Graphs JO - Discrete mathematics & theoretical computer science PY - 2017-2018 VL - 19 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-8/ DO - 10.23638/DMTCS-19-3-8 LA - en ID - DMTCS_2017_19_3_a9 ER -
%0 Journal Article %A Bharathi, Arpitha P. %A De, Minati %A Lahiri, Abhiruk %T Circular Separation Dimension of a Subclass of Planar Graphs %J Discrete mathematics & theoretical computer science %D 2017-2018 %V 19 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-8/ %R 10.23638/DMTCS-19-3-8 %G en %F DMTCS_2017_19_3_a9
Bharathi, Arpitha P.; De, Minati; Lahiri, Abhiruk. Circular Separation Dimension of a Subclass of Planar Graphs. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3. doi: 10.23638/DMTCS-19-3-8
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