scholarly journals The lower bound of the r-dynamic chromatic number of corona product by wheel graphs

2018 ◽  
Author(s):  
Arika Indah Kristiana ◽  
M. Imam Utoyo ◽  
Dafik
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Wheel Graphs ◽  
Corona Product

r-Dynamic coloring of the corona product of graphs

2020 ◽  
Vol 12 (02) ◽  
pp. 2050019
Author(s):  
Arika Indah Kristiana ◽  
M. Imam Utoyo ◽  
Ridho Alfarisi ◽  
Dafik
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Product Of Graphs ◽  
Corona Product

Let [Formula: see text] be a graph. A proper [Formula: see text]-coloring of graph [Formula: see text] is [Formula: see text]-dynamic coloring if for every [Formula: see text], the neighbors of vertex [Formula: see text] receive at least min[Formula: see text] different colors. The minimum [Formula: see text] such that graph [Formula: see text] has [Formula: see text]-dynamic [Formula: see text] coloring is called the [Formula: see text]-dynamic chromatic number, denoted by [Formula: see text]. In this paper, we study the [Formula: see text]-dynamic coloring of corona product of graph. The corona product of graph is obtained by taking a number of vertices [Formula: see text] copy of [Formula: see text], and making the [Formula: see text]th of [Formula: see text] adjacent to every vertex of the [Formula: see text]th copy of [Formula: see text]. We obtain the lower bound of [Formula: see text]-dynamic chromatic number of corona product of graphs and some exact value.

scholarly journals On r-dynamic coloring of comb graphs

2021 ◽  
Vol 27 (2) ◽  
pp. 191-200
Author(s):  
K. Kalaiselvi ◽  
◽  
N. Mohanapriya ◽  
J. Vernold Vivin ◽  
◽  
...  
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Upper Bound ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Middle Graph ◽  
Different Color

An r-dynamic coloring of a graph G is a proper coloring of G such that every vertex in V(G) has neighbors in at least $\min\{d(v),r\}$ different color classes. The r-dynamic chromatic number of graph G denoted as $\chi_r (G)$, is the least k such that G has a coloring. In this paper we obtain the r-dynamic chromatic number of the central graph, middle graph, total graph, line graph, para-line graph and sub-division graph of the comb graph $P_n\odot K_1$ denoted by $C(P_n\odot K_1), M(P_n\odot K_1), T(P_n\odot K_1), L(P_n\odot K_1), P(P_n\odot K_1)$ and $S(P_n\odot K_1)$ respectively by finding the upper bound and lower bound for the r-dynamic chromatic number of the Comb graph.

scholarly journals An improved lower bound for the radio k-chromatic number of the hypercube Qn

2010 ◽  
Vol 60 (7) ◽  
pp. 2131-2140 ◽  
Author(s):  
Srinivasa Rao Kola ◽  
Pratima Panigrahi
Keyword(s):  
Lower Bound ◽  
Chromatic Number

scholarly journals A new lower bound for the chromatic number of general Kneser hypergraphs

2018 ◽  
Vol 71 ◽  
pp. 229-245 ◽  
Author(s):  
Roya Abyazi Sani ◽  
Meysam Alishahi
Keyword(s):  
Lower Bound ◽  
Chromatic Number

THE HARMONIOUS CHROMATIC NUMBER OF A COLLECTION OF WHEEL GRAPHS

2016 ◽  
Vol 100 (9) ◽  
pp. 1487-1503
Author(s):  
W. Charoenpanitseri ◽  
P. Chanthaweeroj
Keyword(s):  
Chromatic Number ◽  
Wheel Graphs

scholarly journals A lower bound on the chromatic number of Mycielski graphs

2001 ◽  
Vol 235 (1-3) ◽  
pp. 79-86 ◽  
Author(s):  
Massimiliano Caramia ◽  
Paolo Dell'Olmo
Keyword(s):  
Lower Bound ◽  
Chromatic Number

scholarly journals Local chromatic number and topology

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Gábor Simonyi ◽  
Gábor Tardos
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Topological Method ◽  
Proper Coloring ◽  
And Topology ◽  
Minimum Number ◽  
International Audience ◽  
Closed Neighborhood

International audience The local chromatic number of a graph, introduced by Erdős et al., is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph. This talk would like to survey some of our recent results on this parameter. We give a lower bound for the local chromatic number in terms of the lower bound of the chromatic number provided by the topological method introduced by Lovász. We show that this bound is tight in many cases. In particular, we determine the local chromatic number of certain odd chromatic Schrijver graphs and generalized Mycielski graphs. We further elaborate on the case of $4$-chromatic graphs and, in particular, on surface quadrangulations.

scholarly journals Colorful Subhypergraphs in Kneser Hypergraphs

10.37236/3573 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Frédéric Meunier
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Bipartite Graphs ◽  
Uniform Hypergraph ◽  
Proper Coloring ◽  
Kneser Graph ◽  
Complete Bipartite Graphs ◽  
Definition Of ◽  
Ky Fan

Using a $\mathbb{Z}_q$-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of what can be the local chromatic number of a uniform hypergraph).

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