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 Scopus citations


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 publicationGraph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers
Number of pages12
ISBN (Print)9783642450426
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)0302-9743
ISSN (Electronic)1611-3349


Other39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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