The maximum k-differential coloring problem

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

Research output: Contribution to journalArticle

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)
Pages (from-to)35-53
Number of pages19
JournalJournal of Discrete Algorithms
Volume45
DOIs
StatePublished - Jul 1 2017

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

Keywords

  • Differential chromatic number
  • Differential coloring
  • Maximum k-differential coloring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

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

In: Journal of Discrete Algorithms, Vol. 45, 01.07.2017, p. 35-53.

Research output: Contribution to journalArticle

Bekos, MA, Kaufmann, M, Kobourov, SG, Stavropoulos, K & Veeramoni, S 2017, 'The maximum k-differential coloring problem', Journal of Discrete Algorithms, vol. 45, pp. 35-53. https://doi.org/10.1016/j.jda.2017.08.001
Bekos, Michael A. ; Kaufmann, Michael ; Kobourov, Stephen G ; Stavropoulos, Konstantinos ; Veeramoni, Sankar. / The maximum k-differential coloring problem. In: Journal of Discrete Algorithms. 2017 ; Vol. 45. pp. 35-53.
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