TY - JOUR
T1 - Edge Intersection Graphs of L-Shaped Paths in Grids
AU - Cameron, Kathie
AU - Chaplick, Steven
AU - Hoàng, Chính T.
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2013
Y1 - 2013
N2 - In this paper we continue the study of the edge intersection graphs of single bend paths on a rectangular grid (i.e., the edge intersection graphs where each vertex is represented by one of the following shapes: {down left corner}, {top left corner}, {down right corner}, {top right corner}). These graphs, called B1- EPG graphs, were first introduced by Golumbic et al (2009) [Golumbic, M. C., M. Lipshteyn and M. Stern, Edge intersection graphs of single bend paths on a grid, Networks 54:3 (2009), 130-138]. We focus on the class [{down left corner}] (the edge intersection graphs of {down left corner}-shapes) and show that testing for membership in [{down left corner}] is NP-complete. We then give a characterization and polytime recognition algorithm for special subclasses of Split∩[{down left corner}]. We also consider the natural subclasses of B1-EPG formed by the subsets of the four single bend shapes (i.e., {{down left corner}}, {{down left corner}, {top left corner}}, {{down left corner}, {top right corner}}, {{down left corner}, {top left corner}, {top right corner}} - note: all other subsets are isomorphic to these up to 90 degree rotation). We observe the expected strict inclusions and incomparability (i.e., [{down left corner}]{subset of with not equal to}[{down left corner}, {top left corner}], [{down left corner}, {top right corner}]{subset of with not equal to}[{down left corner}, {top left corner}, {top right corner}]{subset of with not equal to}B1-EPG and [{down left corner}, {top left corner}] is incomparable with [{down left corner}, {top right corner}]).
AB - In this paper we continue the study of the edge intersection graphs of single bend paths on a rectangular grid (i.e., the edge intersection graphs where each vertex is represented by one of the following shapes: {down left corner}, {top left corner}, {down right corner}, {top right corner}). These graphs, called B1- EPG graphs, were first introduced by Golumbic et al (2009) [Golumbic, M. C., M. Lipshteyn and M. Stern, Edge intersection graphs of single bend paths on a grid, Networks 54:3 (2009), 130-138]. We focus on the class [{down left corner}] (the edge intersection graphs of {down left corner}-shapes) and show that testing for membership in [{down left corner}] is NP-complete. We then give a characterization and polytime recognition algorithm for special subclasses of Split∩[{down left corner}]. We also consider the natural subclasses of B1-EPG formed by the subsets of the four single bend shapes (i.e., {{down left corner}}, {{down left corner}, {top left corner}}, {{down left corner}, {top right corner}}, {{down left corner}, {top left corner}, {top right corner}} - note: all other subsets are isomorphic to these up to 90 degree rotation). We observe the expected strict inclusions and incomparability (i.e., [{down left corner}]{subset of with not equal to}[{down left corner}, {top left corner}], [{down left corner}, {top right corner}]{subset of with not equal to}[{down left corner}, {top left corner}, {top right corner}]{subset of with not equal to}B1-EPG and [{down left corner}, {top left corner}] is incomparable with [{down left corner}, {top right corner}]).
U2 - 10.1016/J.ENDM.2013.10.057
DO - 10.1016/J.ENDM.2013.10.057
M3 - Article
SN - 1571-0653
VL - 44
SP - 363
EP - 369
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -