Zero-one law for random subgraphs of some distance graphs with vertices in $ \mathbb Z^n$

2016 ◽  
Vol 207 (3) ◽  
pp. 458-478
Author(s):  
S N Popova
Keyword(s):  
Distance Graphs ◽  
Random Subgraphs

Independence numbers and chromatic numbers of the random subgraphs of some distance graphs

2015 ◽  
Vol 206 (10) ◽  
pp. 1340-1374 ◽  
Author(s):  
L I Bogolubsky ◽  
A S Gusev ◽  
M M Pyaderkin ◽  
A M Raigorodskii
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs ◽  
Random Subgraphs ◽  
Independence Numbers

New Results on Edge Rotation Distance Graphs

2016 ◽  
Vol 6 (1) ◽  
pp. 81
Author(s):  
Medha Itagi Huilgol ◽  
Chitra Ramprakash
Keyword(s):  
Distance Graphs

S-packing colorings of distance graphs G(Z,{2,t})

2021 ◽  
Vol 298 ◽  
pp. 143-154
Author(s):  
Boštjan Brešar ◽  
Jasmina Ferme ◽  
Karolína Kamenická
Keyword(s):  
Distance Graphs

Density of sets with missing differences and applications

2021 ◽  
Vol 71 (3) ◽  
pp. 595-614
Author(s):  
Ram Krishna Pandey ◽  
Neha Rai
Keyword(s):  
Number Theory ◽  
Asymptotic Density ◽  
Theory Problem ◽  
Distance Graphs ◽  
Positive Integers ◽  
Infinite Set

Abstract For a given set M of positive integers, a well-known problem of Motzkin asks to determine the maximal asymptotic density of M-sets, denoted by μ(M), where an M-set is a set of non-negative integers in which no two elements differ by an element in M. In 1973, Cantor and Gordon find μ(M) for |M| ≤ 2. Partial results are known in the case |M| ≥ 3 including some results in the case when M is an infinite set. Motivated by some 3 and 4-element families already discussed by Liu and Zhu in 2004, we study μ(M) for two families namely, M = {a, b,a + b, n(a + b)} and M = {a, b, b − a, n(b − a)}. For both of these families, we find some exact values and some bounds on μ(M). This number theory problem is also related to various types of coloring problems of the distance graphs generated by M. So, as an application, we also study these coloring parameters associated with these families.

Independence numbers and chromatic numbers of some distance graphs

2015 ◽  
Vol 51 (2) ◽  
pp. 165-176 ◽  
Author(s):  
A. V. Bobu ◽  
O. A. Kostina ◽  
A. E. Kupriyanov
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs ◽  
Independence Numbers

scholarly journals Chromatic numbers of exact distance graphs

2019 ◽  
Vol 134 ◽  
pp. 143-163 ◽  
Author(s):  
Jan van den Heuvel ◽  
H.A. Kierstead ◽  
Daniel A. Quiroz
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs
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