Name
Abstract | ||
|---|---|---|
We prove that for all positive integers nand k, there exists an integer N = N(n, k) satisfying the following. If U is a set of k nonzero vectors in the plane and J(U) is the set of all line segments in direction u for some u is an element of U, then for every N families F-1, ..., F-N, each consisting of n mutually disjoint segments in J(U), there is a set {A(1), ..., A(n)} of n disjoint segments in boolean OR(1 <= i <= N) F-i and distinct integers p(1), ..., p(n) is an element of {1, ..., N} satisfying that A(j) is an element of F-pj for all j is an element of {1, ..., n}. We generalize this property for underlying lines on fixed k directions to k families of simple curves with certain conditions. (C) 2021 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.disc.2021.112621 | DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
Line segments, System of disjoint representatives, Rainbow independent sets | Journal | 344 |
Issue | ISSN | Citations |
12 | 0012-365X | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jin-ha Kim | 1 | 329 | 18.78 |
| Minki Kim | 2 | 0 | 0.34 |
| O-Joung Kwon | 3 | 0 | 0.34 |