Results 111 to 120 of about 9,106,907 (129)
The Packing Chromatic Number of Hypercubes [PDF]
Discrete Applied Mathematics, 2015 The packing chromatic number χρ (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 leasti+1. Goddard et al.
Mario Valencia-Pabon
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On the Packing Chromatic Number of Cartesian Products, Hexagonal Lattice, and Trees
Discrete Applied Mathematics, 2007 The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths.
Boštjan Brešar +2 more
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The Packing Chromatic Number of the Infinite Square Lattice Is Between 13 and 15 [PDF]
Discrete Applied Mathematics, 2017 Using a SAT-solver on top of a partial previously-known solution we improve the upper bound of the packing chromatic number of the infinite square lattice from 17 to 15. We discuss the merits of SAT-solving for this kind of problem as well as compare the
Barnaby Martin +2 more
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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 ...
Mika Olsen +2 more
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A Note on the Packing Chromatic Number of Lexicographic Products [PDF]
Discrete Applied Mathematics, 2021 6 pages, 1 figure, 9 ...
Iztok Peterin
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On the Packing Chromatic Number of Some Lattices
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Douglas Frank Rall, Arthur Finbow
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Packing Chromatic Number of Distance Graphs
Discrete Applied Mathematics, 2012 13 pages, 3 ...
Bernard Lidický +2 more
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Packing Chromatic Number Under Local Changes in a Graph
Discrete Mathematics, 2017 The packing chromatic number $χ_ρ(G)$ of a graph $G$ is the smallest integer $k$ such that there exists a $k$-vertex coloring of $G$ in which any two vertices receiving color $i$ are at distance at least $i+1$. It is proved that in the class of subcubic graphs the packing chromatic number is bigger than $13$, thus answering an open problem from ...
Boštjan Brešar +2 more
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The Exponential Growth of the Packing Chromatic Number of Iterated Mycielskians
Discrete Applied Mathematics, 2023A \(k\)-packing coloring of a graph \(G\) with vertex set \(V\), for a given integer \(k\), is a mapping \(f\colon V\rightarrow \{1,\dots,k\}\) such that for any two distinct vertices \(u\) and \(v\), if \(f(u)=f(v)=i\), then \(g_G(u,v)>i\), where \(d_G(u,v)\) is the distance of \(u\) and \(v\) in \(G\).
Ez-Zobair Bidine +2 more
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The Chromatic Number of the Two-packing of a Forest
1997A two-packing of a graph G is a bijection σ : V(G) → V(G) such that for every two adjacent vertices a, b € V(G) the vertices σ(a)) and σ(b) are not adjacent. It is known [2], [6] that every forest G which is not a star has a two packing σ. If F σ is the graph whose vertices are the vertices of G and in which two vertices a, b are adjacent if and only ...
Hong Wang, Norbert Sauer
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