AuthorBekos, Michael A.
Kobourov, Stephen G.
AffiliationDepartment of Computer Science – University of Arizona, Tucson AZ, USA
MetadataShow full item record
PublisherELSEVIER SCIENCE BV
CitationThe maximum k-differential coloring problem 2017, 45:35 Journal of Discrete Algorithms
JournalJournal of Discrete Algorithms
Rights© 2017 Elsevier B.V. All rights reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractGiven an n-vertex graph Gand two positive integers d, k is an element of 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 (left perpendicular 2n/3 right pendicular, 2n)-differential coloring problem, even in the case where the input graph is planar.
NotePre-print submitted, no embargo
VersionFinal accepted manuscript