Threshold-coloring and unit-cube contact representation of graphs

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

doi:10.1007/978-3-642-45043-3_4

Threshold-coloring and unit-cube contact representation of graphs

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

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

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 language	English (US)
Title of host publication	Graph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers
Publisher	Springer-Verlag
Pages	26-37
Number of pages	12
ISBN (Print)	9783642450426
DOIs	https://doi.org/10.1007/978-3-642-45043-3_4
State	Published - 2013
Event	39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013 - Lubeck, Germany Duration: Jun 19 2013 → Jun 21 2013

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8165 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013
Country/Territory	Germany
City	Lubeck
Period	6/19/13 → 6/21/13

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-45043-3_4

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 Graph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers (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 et al.
Graph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers. 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 proceeding › Conference contribution

Alam, MJ, Chaplick, S, Fijavž, G, Kaufmann, M, Kobourov, SG & Pupyrev, S 2013, Threshold-coloring and unit-cube contact representation of graphs. in Graph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers. 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 Graph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers. Springer-Verlag. 2013. p. 26-37. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-45043-3_4

Alam, Md Jawaherul ; Chaplick, Steven ; Fijavž, Gašper et al. / Threshold-coloring and unit-cube contact representation of graphs. Graph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers. 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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Threshold-coloring and unit-cube contact representation of graphs

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