Threshold-coloring and unit-cube contact representation of graphs

Md Jawaherul Alam, Steven Chaplick, Gašper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey Pupyrev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages26-37
Number of pages12
Volume8165 LNCS
ISBN (Print)9783642450426
DOIs
StatePublished - 2013
Event39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013 - Lubeck, Germany
Duration: Jun 19 2013Jun 21 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8165 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013
CountryGermany
CityLubeck
Period6/19/136/21/13

Fingerprint

Unit cube
Coloring
Colouring
Planar graph
Contact
Color
Graph in graph theory
Grid Graph
Imply
Spanning Subgraph
NP-completeness
Polynomials
Polynomial-time Algorithm
Cycle
Integer
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alam, M. J., Chaplick, S., Fijavž, G., Kaufmann, M., Kobourov, S. G., & Pupyrev, S. (2013). Threshold-coloring and unit-cube contact representation of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8165 LNCS, pp. 26-37). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8165 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-45043-3_4

Threshold-coloring and unit-cube contact representation of graphs. / Alam, Md Jawaherul; Chaplick, Steven; Fijavž, Gašper; Kaufmann, Michael; Kobourov, Stephen G; Pupyrev, Sergey.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8165 LNCS Springer Verlag, 2013. p. 26-37 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8165 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Alam, MJ, Chaplick, S, Fijavž, G, Kaufmann, M, Kobourov, SG & Pupyrev, S 2013, Threshold-coloring and unit-cube contact representation of graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8165 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8165 LNCS, Springer Verlag, pp. 26-37, 39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013, Lubeck, Germany, 6/19/13. https://doi.org/10.1007/978-3-642-45043-3_4
Alam MJ, Chaplick S, Fijavž G, Kaufmann M, Kobourov SG, Pupyrev S. Threshold-coloring and unit-cube contact representation of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8165 LNCS. Springer Verlag. 2013. p. 26-37. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-45043-3_4
Alam, Md Jawaherul ; Chaplick, Steven ; Fijavž, Gašper ; Kaufmann, Michael ; Kobourov, Stephen G ; Pupyrev, Sergey. / Threshold-coloring and unit-cube contact representation of graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8165 LNCS Springer Verlag, 2013. pp. 26-37 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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