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

Bounds on Borsuk Numbers in Distance Graphs of a Special Type

2021 ◽  
Vol 57 (2) ◽  
pp. 136-142
Author(s):  
A. V. Berdnikov ◽  
A.M. Raigorodskii
Keyword(s):  
Distance Graphs

scholarly journals Chromatic numbers of integer distance graphs

2001 ◽  
Vol 233 (1-3) ◽  
pp. 239-246 ◽  
Author(s):  
Arnfried Kemnitz ◽  
Massimiliano Marangio
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs

Chromatic number of distance graphs generated by the sets {2,3,x,y}

2012 ◽  
Vol 25 (4) ◽  
pp. 680-693 ◽  
Author(s):  
Daphne Der-Fen Liu ◽  
Aileen Sutedja
Keyword(s):  
Chromatic Number ◽  
Distance Graphs
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