Happy edges: Threshold-coloring of regular lattices

Md Jawaherul Alam, Stephen G Kobourov, Sergey Pupyrev, Jackson Toeniskoetter

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

3 Citations (Scopus)

Abstract

We study a graph coloring problem motivated by a fun Sudoku-style puzzle. Given a bipartition of the edges of a graph into near and far sets and an integer threshold t, a threshold-coloring of the graph is an assignment of integers to the vertices so that endpoints of near edges differ by t or less, while endpoints of far edges differ by more than t. We study threshold-coloring of tilings of the plane by regular polygons, known as Archimedean lattices, and their duals, the Laves lattices. We prove that some are threshold-colorable with constant number of colors for any edge labeling, some require an unbounded number of colors for specific labelings, and some are not threshold-colorable.

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
Pages28-39
Number of pages12
Volume8496 LNCS
ISBN (Print)9783319078892
DOIs
StatePublished - 2014
Event7th International Conference on Fun with Algorithms, FUN 2014 - Sicily, Italy
Duration: Jul 1 2014Jul 3 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8496 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Conference on Fun with Algorithms, FUN 2014
CountryItaly
CitySicily
Period7/1/147/3/14

Fingerprint

Coloring
Colouring
Labeling
Color
Edge Labeling
Regular polygon
Integer
Graph Coloring
Graph in graph theory
Tiling
Assignment

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alam, M. J., Kobourov, S. G., Pupyrev, S., & Toeniskoetter, J. (2014). Happy edges: Threshold-coloring of regular lattices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8496 LNCS, pp. 28-39). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8496 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-07890-8_3

Happy edges : Threshold-coloring of regular lattices. / Alam, Md Jawaherul; Kobourov, Stephen G; Pupyrev, Sergey; Toeniskoetter, Jackson.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8496 LNCS Springer Verlag, 2014. p. 28-39 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8496 LNCS).

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

Alam, MJ, Kobourov, SG, Pupyrev, S & Toeniskoetter, J 2014, Happy edges: Threshold-coloring of regular lattices. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8496 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8496 LNCS, Springer Verlag, pp. 28-39, 7th International Conference on Fun with Algorithms, FUN 2014, Sicily, Italy, 7/1/14. https://doi.org/10.1007/978-3-319-07890-8_3
Alam MJ, Kobourov SG, Pupyrev S, Toeniskoetter J. Happy edges: Threshold-coloring of regular lattices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8496 LNCS. Springer Verlag. 2014. p. 28-39. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-07890-8_3
Alam, Md Jawaherul ; Kobourov, Stephen G ; Pupyrev, Sergey ; Toeniskoetter, Jackson. / Happy edges : Threshold-coloring of regular lattices. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8496 LNCS Springer Verlag, 2014. pp. 28-39 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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