The maximum k-differential coloring problem

Michael A. Bekos, Michael Kaufmann, Stephen G Kobourov, Sankar Veeramoni

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

Abstract

Given an n-vertex graph G and two positive integers d, k ∈ N, the (d, kn)-differential coloring problem asks for a coloring of the vertices of G (if one exists) with distinct numbers from 1 to kn (treated as colors), such that the minimum difference between the two colors of any adjacent vertices is at least d. While it was known that the problem of determining whether a general graph is (2, n)-differential colorable is NP-complete, our main contribution is a complete characterization of bipartite, planar and outerplanar graphs that admit (2, n)-differential colorings. For practical reasons, we also consider color ranges larger than n, i.e., k > 1. We show that it is NP-complete to determine whether a graph admits a (3, 2n)-differential coloring. The same negative result holds for the (⌊2n/3⌋, 2n)-differential coloring problem, even in the case where the input graph is planar.

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
Pages115-127
Number of pages13
Volume8939
ISBN (Print)9783662460771
StatePublished - 2015
Event41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015 - Pec pod Sněžkou, Czech Republic
Duration: Jan 24 2015Jan 29 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8939
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015
CountryCzech Republic
CityPec pod Sněžkou
Period1/24/151/29/15

Fingerprint

Coloring
Colouring
Graph in graph theory
Color
NP-complete problem
Outerplanar Graph
Bipartite Graph
Planar graph
Adjacent
Distinct
Integer
Vertex of a graph
Range of data

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bekos, M. A., Kaufmann, M., Kobourov, S. G., & Veeramoni, S. (2015). The maximum k-differential coloring problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8939, pp. 115-127). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8939). Springer Verlag.

The maximum k-differential coloring problem. / Bekos, Michael A.; Kaufmann, Michael; Kobourov, Stephen G; Veeramoni, Sankar.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8939 Springer Verlag, 2015. p. 115-127 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8939).

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

Bekos, MA, Kaufmann, M, Kobourov, SG & Veeramoni, S 2015, The maximum k-differential coloring problem. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8939, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8939, Springer Verlag, pp. 115-127, 41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015, Pec pod Sněžkou, Czech Republic, 1/24/15.
Bekos MA, Kaufmann M, Kobourov SG, Veeramoni S. The maximum k-differential coloring problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8939. Springer Verlag. 2015. p. 115-127. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Bekos, Michael A. ; Kaufmann, Michael ; Kobourov, Stephen G ; Veeramoni, Sankar. / The maximum k-differential coloring problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8939 Springer Verlag, 2015. pp. 115-127 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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