Results 11 to 20 of about 24,121 (267)

Packing Coloring of Hypercubes with Extended Hamming Codes

Discrete Applied Mathematics
A {\em packing coloring} of a graph $G$ is a mapping assigning a positive integer (a color) to every vertex of $G$ such that every two vertices of color $k$ are at distance at least $k+1$. The least number of colors needed for a packing coloring of $G$ is called the {\em packing chromatic number} of $G$.
Petr Gregor, Jaka Kranjc, Borut Lužar, Kenny Štorgel   +3 more
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Packing coloring of generalized Sierpinski graphs

Discrete Mathematics & Theoretical Computer Science, 2018
The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $c$ such that the vertex set $V(G)$ can be partitioned into sets $X_1, . . . , X_c$, with the condition that vertices in $X_i$ have pairwise distance greater than $i$. In this paper, we consider the packing chromatic number of several families of Sierpinski-type graphs.
Danilo Korže, Aleksander Vesel
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Packing colorings of subcubic outerplanar graphs [PDF]

Aequationes mathematicae, 2020
Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $(1,2,
Boštjan Brešar, Nicolas Gastineau, Olivier Togni   +2 more
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Sphere packing proper colorings of an expander graph [PDF]

IEEE Transactions on Information Theory
23 pages, 2 ...
Honglin Zhu
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Grundy packing coloring of graphs

Discrete Applied Mathematics
16 pages, 5 figures, 6 tables, 37 ...
Didem Gözüpek, Iztok Peterin
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Packing edge-colorings of subcubic outerplanar graphs [PDF]

For a sequence $S = (s_1, s_2, \ldots, s_k)$ of non-decreasing positive integers, an $S$-packing edge-coloring (S-coloring) of a graph $G$ is a partition of $E(G)$ into $E_1, E_2, \ldots, E_k$ such that the distance between each pair of distinct edges $e_1,e_2 \in E_i$, $1 \le i \le k$, is at least $s_i + 1$.
S. Li, Yifan Li, Xujun Liu
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On packing total coloring [PDF]

In this paper, we introduce a new concept in graph coloring, namely the \textit{packing total coloring}, which extends the idea of packing coloring to both the vertices and the edges of a given graph. More precisely, for a graph $G$, a packing total coloring is a mapping $c: V(G) \cup E(G) \rightarrow \{1, 2, \ldots\}$ with the property that for any ...
Jasmina Ferme, Daša Štesl
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Facial packing edge-coloring of plane graphs

Discrete Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Czap, Július, Jendrol', Stanislav
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Modeling the packing coloring problem of graphs

Applied Mathematical Modelling, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shao, Zehui, Vesel, Aleksander
openaire   +4 more sources

Further results and questions on S-packing coloring of subcubic graphs [PDF]

Discrete Mathematics
Maidoun Mortada, Olivier Togni
exaly   +4 more sources