@inproceedings{09a010a689334fbcb12c5aa3545c8afc,

title = "Threshold-Coloring and Unit-Cube Contact Representation of Graphs",

abstract = "We study threshold coloring of graphs where the vertex colors, represented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply 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. We show the np-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.keywordsplanar graphinternal vertexgraph classcontact representationbottom facethese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.",

author = "Alam, {Md Jawaherul} and Steven Chaplick and Michael Kaufmann and Gasper Fijavz and Kobourov, {Stephen G.} and Sergey Pupyrev",

note = "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.",

year = "2013",

doi = "10.1007/978-3-642-45043-3_4",

language = "English",

volume = "8165",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature Switzerland AG",

pages = "26--37",

editor = "A. Brandst{\"a}dt and A. Jansen and R. Reischuk",

booktitle = "Graph-Theoretic Concepts in Computer Science. WG 2013",

}