scholarly journals On the packing chromatic number of subcubic outerplanar graphs

2019 ◽  
Vol 255 ◽  
pp. 209-221 ◽  
Author(s):  
Nicolas Gastineau ◽  
Přemysl Holub ◽  
Olivier Togni
Keyword(s):  
Chromatic Number ◽  
Outerplanar 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 Relaxed game chromatic number of trees and outerplanar graphs

2004 ◽  
Vol 281 (1-3) ◽  
pp. 209-219 ◽  
Author(s):  
Wenjie He ◽  
Jiaojiao Wu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number

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 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 Strong Oriented Chromatic Number of Planar Graphs without Short Cycles

2008 ◽  
Vol Vol. 10 no. 1 ◽  
Author(s):  
Mickael Montassier ◽  
Pascal Ochem ◽  
Alexandre Pinlou
Keyword(s):  
Abelian Group ◽  
Chromatic Number ◽  
Planar Graphs ◽  
Oriented Graph ◽  
Minimal Order ◽  
Outerplanar Graphs ◽  
International Audience

International audience Let M be an additive abelian group. An M-strong-oriented coloring of an oriented graph G is a mapping f from V(G) to M such that f(u) <> j(v) whenever uv is an arc in G and f(v)−f(u) <> −(f(t)−f(z)) whenever uv and zt are two arcs in G. The strong oriented chromatic number of an oriented graph is the minimal order of a group M such that G has an M-strong-oriented coloring. This notion was introduced by Nesetril and Raspaud [Ann. Inst. Fourier, 49(3):1037-1056, 1999]. We prove that the strong oriented chromatic number of oriented planar graphs without cycles of lengths 4 to 12 (resp. 4 or 6) is at most 7 (resp. 19). Moreover, for all i ≥ 4, we construct outerplanar graphs without cycles of lengths 4 to i whose oriented chromatic number is 7.

scholarly journals Enumeration and Asymptotic Properties of Unlabeled Outerplanar Graphs

10.37236/984 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Manuel Bodirsky ◽  
Éric Fusy ◽  
Mihyun Kang ◽  
Stefan Vigerske
Keyword(s):  
Chromatic Number ◽  
Polynomial Time ◽  
Asymptotic Properties ◽  
Statistical Properties ◽  
Cycle Index ◽  
Outerplanar Graphs ◽  
Analytic Combinatorics ◽  
Exact Number ◽  
Asymptotic Number

We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number $g_{n}$ of unlabeled outerplanar graphs on $n$ vertices can be computed in polynomial time, and $g_{n}$ is asymptotically $g\, n^{-5/2}\rho^{-n}$, where $g\approx0.00909941$ and $\rho^{-1}\approx7.50360$ can be approximated. Using our enumerative results we investigate several statistical properties of random unlabeled outerplanar graphs on $n$ vertices, for instance concerning connectedness, the chromatic number, and the number of edges. To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics.

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

scholarly journals The 6-relaxed game chromatic number of outerplanar graphs

2008 ◽  
Vol 308 (24) ◽  
pp. 5974-5980 ◽  
Author(s):  
Jiaojiao Wu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number
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