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 Scopus citations


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 publicationFun with Algorithms - 7th International Conference, FUN 2014, Proceedings
Number of pages12
ISBN (Print)9783319078892
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)0302-9743
ISSN (Electronic)1611-3349


Other7th International Conference on Fun with Algorithms, FUN 2014

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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