Results 11 to 20 of about 255,219 (274)
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
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Online Vector Bin Packing and Hypergraph Coloring Illuminated: Simpler Proofs and New Connections [PDF]
Latin-American Algorithms, Graphs and Optimization Symposium, 2023 This paper studies the online vector bin packing (OVBP) problem and the related problem of online hypergraph coloring (OHC). Firstly, we use a double counting argument to prove an upper bound of the competitive ratio of $FirstFit$ for OVBP.
Yaqiao Li, D. Pankratov
semanticscholar +2 more sources
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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Grundy packing coloring of graphs
Discrete Applied Mathematics16 pages, 5 figures, 6 tables, 37 ...
Didem Gözüpek, Iztok Peterin
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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 +2 more
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Sphere packing proper colorings of an expander graph [PDF]
IEEE Transactions on Information Theory23 pages, 2 ...
Honglin Zhu
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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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Packing Coloring of Hypercubes with Extended Hamming Codes
Discrete Applied MathematicsA {\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 +3 more
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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 colorings of distance graphs
Discrete Applied Mathematics, 2014 The {\em packing chromatic number} $ _ (G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\{1,2,\ldots ,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. This paper studies the packing chromatic number of infinite distance graphs $G(\mathbb{Z},D)$, i.e.
Barajas +14 more
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