scholarly journals Packing chromatic number of cubic graphs

2018 ◽  
Vol 341 (2) ◽  
pp. 474-483 ◽  
Author(s):  
József Balogh ◽  
Alexandr Kostochka ◽  
Xujun Liu
Keyword(s):  
Chromatic Number ◽  
Cubic Graphs ◽  
Packing Chromatic Number

scholarly journals Packing Chromatic Number of Subdivisions of Cubic Graphs

2019 ◽  
Vol 35 (2) ◽  
pp. 513-537 ◽  
Author(s):  
József Balogh ◽  
Alexandr Kostochka ◽  
Xujun Liu
Keyword(s):  
Chromatic Number ◽  
Cubic Graphs ◽  
Packing Chromatic Number

Packing Chromatic Number of Cycle Related Graphs

2014 ◽  
Vol 4 (1) ◽  
pp. 27
Author(s):  
Albert William ◽  
Roy Santiago ◽  
Indra Rajasingh
Keyword(s):  
Chromatic Number ◽  
Packing Chromatic Number

Packing coloring on subdivision-vertex and subdivision-edge join of cycle Cm with path Pn

2020 ◽  
pp. 627-634
Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Packing Chromatic Number ◽  
Cycle Graph

The packing chromatic number $\chi_\rho$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, the authors find the packing chromatic number of subdivision vertex join of cycle graph with path graph and subdivision edge join of cycle graph with path graph.

scholarly journals The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs

2021 ◽  
Vol 33 (5) ◽  
pp. 66-73
Author(s):  
B. CHALUVARAJU ◽  
◽  
M. KUMARA ◽  
Keyword(s):  
Chromatic Number ◽  
Pairwise Distance ◽  
Circulant Graphs ◽  
Vertex Set ◽  
Packing Chromatic Number ◽  
Jump Sizes

The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}

scholarly journals On the equitable total chromatic number of cubic graphs

2016 ◽  
Vol 209 ◽  
pp. 84-91 ◽  
Author(s):  
S. Dantas ◽  
C.M.H. de Figueiredo ◽  
G. Mazzuoccolo ◽  
M. Preissmann ◽  
V.F. dos Santos ◽  
...  
Keyword(s):  
Chromatic Number ◽  
Cubic Graphs ◽  
Total Chromatic Number

scholarly journals Snarks with total chromatic number 5

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Gunnar Brinkmann ◽  
Myriam Preissmann ◽  
Diana Sasaki
Keyword(s):  
Chromatic Number ◽  
Edge Coloring ◽  
Total Coloring ◽  
Computer Search ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Total Chromatic Number ◽  
Vertex Number ◽  
Chordless Cycle

Graph Theory International audience A k-total-coloring of G is an assignment of k colors to the edges and vertices of G, so that adjacent and incident elements have different colors. The total chromatic number of G, denoted by χT(G), is the least k for which G has a k-total-coloring. It was proved by Rosenfeld that the total chromatic number of a cubic graph is either 4 or 5. Cubic graphs with χT = 4 are said to be Type 1, and cubic graphs with χT = 5 are said to be Type 2. Snarks are cyclically 4-edge-connected cubic graphs that do not allow a 3-edge-coloring. In 2003, Cavicchioli et al. asked for a Type 2 snark with girth at least 5. As neither Type 2 cubic graphs with girth at least 5 nor Type 2 snarks are known, this is taking two steps at once, and the two requirements of being a snark and having girth at least 5 should better be treated independently. In this paper we will show that the property of being a snark can be combined with being Type 2. We will give a construction that gives Type 2 snarks for each even vertex number n≥40. We will also give the result of a computer search showing that among all Type 2 cubic graphs on up to 32 vertices, all but three contain an induced chordless cycle of length 4. These three exceptions contain triangles. The question of the existence of a Type 2 cubic graph with girth at least 5 remains open.

Packing Chromatic Number of Base-3 Sierpiński Graphs

2015 ◽  
Vol 32 (4) ◽  
pp. 1313-1327 ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Douglas F. Rall
Keyword(s):  
Chromatic Number ◽  
Sierpiński Graphs ◽  
Packing Chromatic Number

scholarly journals On the packing chromatic number of Moore graphs

2021 ◽  
Vol 289 ◽  
pp. 185-193
Author(s):  
J. Fresán-Figueroa ◽  
D. González-Moreno ◽  
M. Olsen
Keyword(s):  
Chromatic Number ◽  
Packing Chromatic Number

Packing chromatic number, $$\mathbf (1, 1, 2, 2) $$ ( 1 , 1 , 2 , 2 ) -colorings, and characterizing the Petersen graph

2017 ◽  
Vol 91 (1) ◽  
pp. 169-184 ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Douglas F. Rall ◽  
Kirsti Wash
Keyword(s):  
Chromatic Number ◽  
Petersen Graph ◽  
Packing Chromatic Number

scholarly journals The packing chromatic number of infinite product graphs

2009 ◽  
Vol 30 (5) ◽  
pp. 1101-1113 ◽  
Author(s):  
Jiří Fiala ◽  
Sandi Klavžar ◽  
Bernard Lidický
Keyword(s):  
Chromatic Number ◽  
Infinite Product ◽  
Product Graphs ◽  
Packing Chromatic Number
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