Name
Abstract | ||
|---|---|---|
For $z_1,z_2,z_3\in\Z^2$, the tristance $d_3(z_1,z_2,z_3)$ is a generalization of the $L_1$-distance on $\mathbb{Z}^2$ to a quality that reflects the relative dispersion of three points rather than two. In this paper we prove that at least 3k2 colors are required to color the points of $\mathbb{Z}^2$, such that the tristance between any three distinct points, colored with the same color, is at least 4k. We prove that 3k2+3k+1 colors are required if the tristance is at least 4k+2. For the first case we show an infinite family of colorings with colors and conjecture that these are the only colorings with 3k2 colors. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S0895480104439589 | SIAM Journal on Discrete Mathematics |
Keywords | Field | DocType |
lattice | Discrete mathematics,Combinatorics,Colored,Lattice (order),Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
18 | 4 | 0895-4801 |
Citations | PageRank | References |
5 | 0.58 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Y. Ben-Haim | 1 | 140 | 8.29 |
| Tuvi Etzion | 2 | 587 | 75.56 |