Results 11 to 20 of about 8,753,370 (220)
Packing chromatic number of distance graphs [PDF]
Discrete Applied Mathematics, 2012 13 pages, 3 ...
Bernard Lidický +2 more
exaly +5 more sources
On the packing chromatic number of some lattices [PDF]
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Douglas Rall, Arthur Finbow
exaly +3 more sources
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees [PDF]
Discrete Applied Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boštjan Brešar +2 more
exaly +9 more sources
Subdivision into i-packings and S-packing chromatic number of some lattices [PDF]
Ars Mathematica Contemporanea, 2015 An $i$-packing in a graph $G$ is a set of vertices at pairwise distance greater than $i$. For a nondecreasing sequence of integers $S=(s\_{1},s\_{2},\ldots)$, the $S$-packing chromatic number of a graph $G$ is the least integer $k$ such that there exists a coloring of $G$ into $k$ colors where each set of vertices colored $i$, $i=1,\ldots, k$, is an $s\
Gastineau, Nicolas +2 more
core +18 more sources
Packing chromatic number of cubic graphs
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xujun Liu +2 more
exaly +3 more sources
The packing chromatic number of infinite product graphs [PDF]
European Journal of Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jirí Fiala 0001 +2 more
openaire +4 more sources
Packing chromatic number of transformation graphs
Thermal Science, 2019 Graph coloring is an assignment of labels called colors to elements of a graph. The packing coloring was introduced by Goddard et al. [1] in 2008 which is a kind of coloring of a graph. This problem is NP-complete for general graphs. In this paper, we consider some transformation graphs and generalized their packing chromatic numbers.
Derya Durgun, Busra Ozen-Dortok
openaire +3 more sources
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
exaly +3 more sources
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
exaly +4 more sources
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
exaly +7 more sources