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Jinha, Kim
이산수학 그룹
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A system of disjoint representatives of line segments with given k directions

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Title
A system of disjoint representatives of line segments with given k directions
Author(s)
JINHA KIM; MINKI KIM; O-JOUNG KWON
Publication Date
2021-12-01
Journal
Discrete Mathematics, v.344, no.12
Publisher
Elsevier B.V.
Abstract
© 2021 Elsevier B.V.We prove that for all positive integers n and 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 JU is the set of all line segments in direction u for some u∈U, then for every N families F1,…,FN, each consisting of n mutually disjoint segments in JU, there is a set {A1,…,An} of n disjoint segments in ⋃1≤i≤NFi and distinct integers p1,…,pn∈{1,…,N} satisfying that Aj∈Fpj for all j∈{1,…,n}. We generalize this property for underlying lines on fixed k directions to k families of simple curves with certain conditions.
URI
https://pr.ibs.re.kr/handle/8788114/10412
DOI
10.1016/j.disc.2021.112621
ISSN
0012-365X
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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