Research output: Contribution to journal › Article › peer-review
On the chromatic numbers of small-dimensional Euclidean spaces. / Cherkashin, Danila; Kulikov, Anatoly; Raigorodskii, Andrei.
In: Discrete Applied Mathematics, Vol. 243, 10.07.2018, p. 125-131.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On the chromatic numbers of small-dimensional Euclidean spaces
AU - Cherkashin, Danila
AU - Kulikov, Anatoly
AU - Raigorodskii, Andrei
PY - 2018/7/10
Y1 - 2018/7/10
N2 - This paper is devoted to the study of the graph sequence Gn=(Vn,En), where Vn is the set of all vectors v∈Rn with coordinates in {−1,0,1} such that |v|=3 and En consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of Gn. As a corollary we get new lower bounds on χ(Rn) and χ(Qn) for small values of n.
AB - This paper is devoted to the study of the graph sequence Gn=(Vn,En), where Vn is the set of all vectors v∈Rn with coordinates in {−1,0,1} such that |v|=3 and En consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of Gn. As a corollary we get new lower bounds on χ(Rn) and χ(Qn) for small values of n.
KW - Chromatic number
KW - Distance graphs
KW - Independence number
KW - R-N
KW - SETS
UR - http://www.scopus.com/inward/record.url?scp=85044308219&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2018.02.005
DO - 10.1016/j.dam.2018.02.005
M3 - Article
AN - SCOPUS:85044308219
VL - 243
SP - 125
EP - 131
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
ER -
ID: 36097989