Results 21 to 30 of about 8,753,370 (220)
An infinite family of subcubic graphs with unbounded packing chromatic number [PDF]
Discrete Mathematics, 2018 Recently, Balogh, Kostochka and Liu in [Packing chromatic number of cubic graphs, Discrete Math.~341 (2018) 474--483] answered in negative the question that was posed in several earlier papers whether the packing chromatic number is bounded in the class of graphs with maximum degree $3$.
Boštjan Brešar
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Bounds for packing chromatic number of some subclasses of trees
Discussiones Mathematicae Graph TheoryK. Mohamed Harith +2 more
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Packing coloring of generalized Sierpinski graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 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, . . .
Danilo Korze, Aleksander Vesel
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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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$K_{\ell}^{-}$-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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On packing chromatic number of subcubic outerplanar graphs
, 2018 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).
Holub, Přemysl +2 more
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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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