Results 11 to 20 of about 965 (204)
On the packing chromatic number of some lattices
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arthur S Finbow, Douglas F Rall
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Packing chromatic number of distance graphs
Discrete Applied Mathematics, 2012 13 pages, 3 ...
Jan Ekstein +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.
József Balogh +2 more
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On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
Discrete Applied Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boštjan Brešar +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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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 Dvorak
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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 performance of different encodings. Further, we improve the lower bound from 12 to 13 again using a
Barnaby Martin +2 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 $3$.
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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