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Independence Number and Packing Coloring of Generalized Mycielski Graphs
Discussiones Mathematicae Graph Theory, 2021 For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1 ...
Bidine Ez Zobair +2 more
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Packing chromatic vertex-critical graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\in [k]$, where vertices in $V_i$ are pairwise at distance at least $i+1$.
Sandi Klavžar, Douglas F. Rall
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Colouring random geometric graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A random geometric graph $G_n$ is obtained as follows. We take $X_1, X_2, \ldots, X_n ∈\mathbb{R}^d$ at random (i.i.d. according to some probability distribution ν on $\mathbb{R}^d$). For $i ≠j$ we join $X_i$ and $X_j$ by an edge if $║X_i - X_j ║< r(n)$.
Colin J. H. McDiarmid, Tobias Müller
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A Note on Packing Chromatic Number of the Square Lattice [PDF]
The Electronic Journal of Combinatorics, 2010 The concept of a packing colouring is related to a frequency assignment problem. The packing chromatic number $\chi_p(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set $V (G)$ can be partitioned into disjoint classes $X_1, \dots, X_k$, where vertices in $X_i$ have pairwise distance greater than $i$.
Roman Soukal, Premysl Holub
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$K_{\ell}^{-}$-factors in graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $K_ℓ^-$ denote the graph obtained from $K_ℓ$ by deleting one edge. We show that for every $γ >0$ and every integer $ℓ≥4$ there exists an integer $n_0=n_0(γ ,ℓ)$ such that every graph $G$ whose order $n≥n_0$ is divisible by $ℓ$ and whose minimum ...
Daniela Kühn, Deryk Osthus
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Packing Chromatic Number of Subdivisions of Cubic Graphs [PDF]
Graphs and Combinatorics, 2019 20 pages, 15 ...
József Balogh +2 more
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PACKING CHROMATIC NUMBER OF CERTAIN GRAPHS [PDF]
International Journal of Pure and Apllied Mathematics, 2013 The packing chromatic number (G) of a graph G is the smallest integer k for which there exists a mapping : V (G) −→ {1,2,...,k} such that any two vertices of color i are at distance at least i + 1. It is a frequency assignment problem used in wireless networks, which is also called broadcasting coloring.
A. William, S. Roy
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Packing Coloring of Some Undirected and Oriented Coronae Graphs
Discussiones Mathematicae Graph Theory, 2017 The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . . , Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in
Laïche Daouya +2 more
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On the packing chromatic number of square and hexagonal lattice
Ars Mathematica Contemporanea, 2013 The packing chromatic number χ ρ ( G ) of a graph G is the smallest integer k such that the vertex set V ( G ) can be partitioned into disjoint classes X 1 , …, X k , with the condition that vertices in X i have pairwise distance greater than i . We show that the packing chromatic number for the hexagonal lattice ℋ
Korže, Danilo, Vesel, Aleksander
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On packing chromatic number of subcubic outerplanar graphs
CoRR, 2017 Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exists subclasses in which the packing chromatic number is finite (and small). These subclasses include subcubic trees, base-3 Sierpi{ń}ski graphs and hexagonal lattices.In this paper we are interested in the packing chromatic ...
Nicolas Gastineau +2 more
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