The maximum k-differential coloring problem

Michael A. Bekos, Michael Kaufmann, Stephen 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 publicationSOFSEM 2015
Subtitle of host publicationTheory and Practice of Computer Science - 41st International Conference on Current Trends in Theory and Practice of Computer Science,
EditorsGiuseppe F. Italiano, Tiziana Margaria-Steffen, Jaroslav Pokorný, Jean-Jacques Quisquater, Roger Wattenhofer
PublisherSpringer-Verlag
Pages115-127
Number of pages13
ISBN (Electronic)9783662460771
DOIs
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)0302-9743
ISSN (Electronic)1611-3349

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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