Geodesic
Graphs of Edge-Intersecting and Non-Splitting One Bend Paths in a Grid
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 1.

Voir la notice de l'article provenant de la source Episciences

The families EPT (resp. EPG) Edge Intersection Graphs of Paths in a tree (resp. in a grid) are well studied graph classes. Recently we introduced the graph classes Edge-Intersecting and Non-Splitting Paths in a Tree ENPT, and in a Grid (ENPG). It was shown that ENPG contains an infinite hierarchy of subclasses that are obtained by restricting the number of bends in the paths. Motivated by this result, in this work we focus on one bend {ENPG} graphs. We show that one bend ENPG graphs are properly included in two bend ENPG graphs. We also show that trees and cycles are one bend ENPG graphs, and characterize the split graphs and co-bipartite graphs that are one bend ENPG. We prove that the recognition problem of one bend ENPG split graphs is NP-complete even in a very restricted subfamily of split graphs. Last we provide a linear time recognition algorithm for one bend ENPG co-bipartite graphs. 
@article{DMTCS_2017_19_1_a14,
     author = {Boyac{\i}, Arman and Ekim, T{\i}naz and Shalom, Mordechai and Zaks, Shmuel},
     title = {Graphs of {Edge-Intersecting} and {Non-Splitting} {One} {Bend} {Paths} in a {Grid}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2017-2018},
     doi = {10.23638/DMTCS-19-1-13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-13/}
}
TY  - JOUR
AU  - Boyacı, Arman
AU  - Ekim, Tınaz
AU  - Shalom, Mordechai
AU  - Zaks, Shmuel
TI  - Graphs of Edge-Intersecting and Non-Splitting One Bend Paths in a Grid
JO  - Discrete mathematics & theoretical computer science
PY  - 2017-2018
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-13/
DO  - 10.23638/DMTCS-19-1-13
LA  - en
ID  - DMTCS_2017_19_1_a14
ER  - 
%0 Journal Article
%A Boyacı, Arman
%A Ekim, Tınaz
%A Shalom, Mordechai
%A Zaks, Shmuel
%T Graphs of Edge-Intersecting and Non-Splitting One Bend Paths in a Grid
%J Discrete mathematics & theoretical computer science
%D 2017-2018
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-13/
%R 10.23638/DMTCS-19-1-13
%G en
%F DMTCS_2017_19_1_a14
Boyacı, Arman; Ekim, Tınaz; Shalom, Mordechai; Zaks, Shmuel. Graphs of Edge-Intersecting and Non-Splitting One Bend Paths in a Grid. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 1. doi : 10.23638/DMTCS-19-1-13. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-13/

Cité par Sources :