Results 21 to 30 of about 1,143 (224)
Packing Coloring of Some Undirected and Oriented Coronae Graphs [PDF]
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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Packing chromatic number of cubic graphs
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xujun Liu +2 more
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The Packing Chromatic Number of the Infinite Square Grid is At Least 14 [PDF]
, 2022 Code corresponding to the paper "The Packing Chromatic Number of the Infinite Square Grid is At Least 14", accepted at SAT'2022. A README file explains how to use it.
Subercaseaux, Bernardo +1 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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Induced odd cycle packing number, independent sets, and chromatic number
Journal of Graph Theory, 2023 AbstractThe induced odd cycle packing number of a graph is the maximum integer such that contains an induced subgraph consisting of pairwise vertex‐disjoint odd cycles. Motivated by applications to geometric graphs, Bonamy et al. proved that graphs of bounded induced odd cycle packing number, bounded Vapnik–Chervonenkis (VC) dimension, and linear ...
Zdenek Dvorák 0001, Jakub Pekárek
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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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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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