Results 1 to 10 of about 965 (204)
Packing chromatic number of certain fan and wheel related graphs
AKCE International Journal of Graphs and Combinatorics, 2017 The packing chromatic number of a graph is the smallest integer for which there exists a mapping such that any two vertices of color are at distance at least .
S. Roy
doaj +3 more sources
A lower bound for the packing chromatic number of the Cartesian product of cycles
Open Mathematics, 2013 Abstract Let G = (V, E) be a simple graph of order n and i be an integer with i ≥ 1. The set X i ⊆ V(G) is called an i-packing if each two distinct vertices in X i are more than i apart. A packing colouring of G is a partition X = {X 1, X 2, …,
Jacobs Yolandé +2 more
doaj +3 more sources
Graphs that are Critical for the Packing Chromatic Number
Discussiones Mathematicae Graph Theory, 2022 Given a graph G, a coloring c : V (G) → {1, …, k} such that c(u) = c(v) = i implies that vertices u and v are at distance greater than i, is called a packing coloring of G.
Brešar Boštjan, Ferme Jasmina
doaj +3 more sources
Discussiones Mathematicae Graph Theory, 2020 If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . .
Brešar Boštjan +3 more
doaj +2 more sources
On the packing chromatic number of Moore graphs [PDF]
Discrete Applied Mathematics, 2021 The \emph{packing chromatic number $χ_ρ(G)$} of a graph $G$ is the smallest integer $k$ for which there exists a vertex coloring $Γ: V(G)\rightarrow \{1,2,\dots , k\}$ such that any two vertices of color $i$ are at distance at least $i + 1$. For $g\in \{6,8,12\}$, $(q+1,g)$-Moore graphs are $(q+1)$-regular graphs with girth $g$ which are the incidence ...
Julian Fresán-Figueroa +2 more
exaly +4 more sources
A note on the packing chromatic number of lexicographic products [PDF]
Discrete Applied Mathematics, 2021 6 pages, 1 figure, 9 ...
Iztok Peterin
exaly +4 more sources
On the packing chromatic number of hypercubes [PDF]
Electronic Notes in Discrete Mathematics, 2013 The packing chromatic number $\chi_\rho(G)$ of a graph $G$ is the smallest integer $k$ needed to proper color the vertices of $G$ in such a way that the distance in $G$ between any two vertices having color $i$ be at least $i+1$. Goddard et al. \cite{Goddard08} found an upper bound for the packing chromatic number of hypercubes $Q_n$.
Pablo Torres, Mario Valencia-Pabon
exaly +4 more sources
Packing chromatic number versus chromatic and clique number [PDF]
Aequationes Mathematicae, 2017 17 pages, 1 ...
Boštjan Brešar +2 more
exaly +4 more sources
On the packing chromatic number of subcubic outerplanar graphs [PDF]
Discrete Applied Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicolas Gastineau +2 more
exaly +4 more sources
The packing chromatic number of hypercubes
Discrete Applied Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pablo Torres, Mario Valencia-Pabon
exaly +4 more sources