Results 21 to 30 of about 9,106,907 (129)
Packing chromatic number of cubic graphs
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
József Balogh +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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List packing number of bounded degree graphs [PDF]
, 2023 We investigate the list packing number of a graph, the least k such that there are always k disjoint proper list-colourings whenever we have lists all of size k associated to the vertices.
Davies, E. +7 more
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The packing chromatic number of infinite product graphs
European Journal of Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jirí Fiala 0001 +2 more
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The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs [PDF]
Journal of Ultra Scientist of Physical Sciences Section A, 2021 The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}
B. CHALUVARAJU, M. KUMARA
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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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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 ...
Gastineau, Nicolas +2 more
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The Packing Chromatic Number of the Infinite Square Grid is 15
, 2023 Abstract A packing k -coloring is a natural variation on the standard notion of graph k -coloring, where vertices are assigned numbers from $$\{1, \ldots , k\}$$
Bernardo Subercaseaux +1 more
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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 $3$.
Bostjan Bresar, Jasmina Ferme
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Packing, hitting, and colouring squares
Journal of Computational GeometryGiven a family of squares in the plane, the packing problem asks for the maximum number $\nu$ of pairwise disjoint squares among them, while the hitting problem asks for the minimum number $\tau$ of points hitting all of them.
Marco Caoduro, András Sebő
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