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 language | English (US) |
|---|---|
| Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher | Springer Verlag |
| Pages | 28-39 |
| Number of pages | 12 |
| Volume | 8496 LNCS |
| ISBN (Print) | 9783319078892 |
| DOIs | |
| State | Published - 2014 |
| Event | 7th International Conference on Fun with Algorithms, FUN 2014 - Sicily, Italy Duration: Jul 1 2014 → Jul 3 2014 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 8496 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 7th International Conference on Fun with Algorithms, FUN 2014 |
|---|---|
| Country | Italy |
| City | Sicily |
| Period | 7/1/14 → 7/3/14 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
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 proceeding › Conference contribution
}
TY - GEN
T1 - Happy edges
T2 - Threshold-coloring of regular lattices
AU - Alam, Md Jawaherul
AU - Kobourov, Stephen G
AU - Pupyrev, Sergey
AU - Toeniskoetter, Jackson
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84903746702&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903746702&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-07890-8_3
DO - 10.1007/978-3-319-07890-8_3
M3 - Conference contribution
AN - SCOPUS:84903746702
SN - 9783319078892
VL - 8496 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 28
EP - 39
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PB - Springer Verlag
ER -