scholarly journals Chromatic numbers of the strong product of odd cycles

2002 ◽  
Vol 11 ◽  
pp. 647-652
Author(s):  
Janez Z̆erovnik
Keyword(s):  
Chromatic Numbers ◽  
Strong Product ◽  
Odd Cycles

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 The independence number of the strong product of odd cycles

1998 ◽  
Vol 182 (1-3) ◽  
pp. 333-336 ◽  
Author(s):  
Aleksander Vesel ◽  
Janez Ẑerovnik
Keyword(s):  
Independence Number ◽  
Strong Product ◽  
Odd Cycles

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

scholarly journals The set chromatic numbers of the middle graph of graphs

2021 ◽  
Vol 1836 (1) ◽  
pp. 012014
Author(s):  
G R J Eugenio ◽  
M J P Ruiz ◽  
M A C Tolentino
Keyword(s):  
Chromatic Numbers ◽  
Middle Graph

scholarly journals Strong product of two S+-valued graphs

2021 ◽  
Vol 1084 (1) ◽  
pp. 012110
Author(s):  
M. Sundar ◽  
M. Chandramouleeswaran
Keyword(s):  
Strong Product

scholarly journals Toll number of the strong product of graphs

2019 ◽  
Vol 342 (3) ◽  
pp. 807-814
Author(s):  
Tanja Gologranc ◽  
Polona Repolusk
Keyword(s):  
Strong Product ◽  
Product Of Graphs

scholarly journals Hamiltonian Cycles in Strong Products of Graphs

1979 ◽  
Vol 22 (3) ◽  
pp. 305-309 ◽  
Author(s):  
J. C. Bermond ◽  
A. Germa ◽  
M. C. Heydemann
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycles ◽  
Strong Product

Abstract. Let denote the graph (k times) where is the strong product of the two graphs G and H. In this paper we prove the conjecture of J. Zaks [3]: For every connected graph G with at least two vertices there exists an integer k = k(G) for which the graph is hamiltonian.

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

Solar-cycle phenomena in cosmic-ray intensity: Differences between even and odd cycles

1988 ◽  
Vol 42 (3) ◽  
pp. 233-244 ◽  
Author(s):  
H. Mavromichalaki ◽  
E. Marmatsouri ◽  
A. Vassilaki
Keyword(s):  
Solar Cycle ◽  
Cosmic Ray ◽  
Cosmic Ray Intensity ◽  
Odd Cycles

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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