TY - JOUR
T1 - Threshold-coloring and unit-cube contact representation of planar graphs
AU - Alam, Md Jawaherul
AU - Chaplick, Steven
AU - Fijavz, Gasper
AU - Michael, Kaufmann
AU - Kobourov, Stephen G.
AU - Pupyrev, Sergey
AU - Toeniskoetter, Jackson
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 - 2017
Y1 - 2017
N2 - In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain unit-cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another. (C) 2015 Elsevier B.V. All rights reserved.
AB - In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain unit-cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another. (C) 2015 Elsevier B.V. All rights reserved.
U2 - 10.1016/J.DAM.2015.09.003
DO - 10.1016/J.DAM.2015.09.003
M3 - Article
VL - 216
SP - 2
EP - 14
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -