Chromatic Numbers of Distance Graphs without Short Odd Cycles in Rational Spaces

2021 ◽  
Vol 109 (5-6) ◽  
pp. 727-734
Author(s):  
Yu. A. Demidovich ◽  
M. E. Zhukovskii
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs ◽  
Odd Cycles

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

scholarly journals Between 2- and 3-Colorability

10.37236/4673 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Alan Frieze ◽  
Wesley Pegden
Keyword(s):  
Positive Integer ◽  
Random Graphs ◽  
The Other ◽  
Chromatic Numbers ◽  
Other Hand ◽  
Odd Cycles

We consider the question of the existence of homomorphisms between $G_{n,p}$ and odd cycles when $p=c/n$, $1<c\leq 4$. We show that for any positive integer $\ell$, there exists $\epsilon=\epsilon(\ell)$ such that if $c=1+\epsilon$ then w.h.p. $G_{n,p}$ has a homomorphism from $G_{n,p}$ to $C_{2\ell+1}$ so long as its odd-girth is at least $2\ell+1$. On the other hand, we show that if $c=4$ then w.h.p. there is no homomorphism from $G_{n,p}$ to $C_5$. Note that in our range of interest, $\chi(G_{n,p})=3$ w.h.p., implying that there is a homomorphism from $G_{n,p}$ to $C_3$.  These results imply the existence of random graphs with circular chromatic numbers $\chi_c$ satisfying $2<\chi_c(G)<2+\delta$ for arbitrarily small $\delta$, and also that $2.5\leq \chi_c(G_{n,\frac 4 n})<3$ w.h.p.

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

On chromatic numbers of close-to-Kneser distance graphs

2016 ◽  
Vol 52 (4) ◽  
pp. 373-390 ◽  
Author(s):  
A. V. Bobu ◽  
A. E. Kupriyanov
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs

scholarly journals Circular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs

1998 ◽  
Vol 19 (4) ◽  
pp. 423-431 ◽  
Author(s):  
G.J. Chang ◽  
L. Huang ◽  
X. Zhu
Keyword(s):  
Chromatic Numbers ◽  
Distance Graphs
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