Aequationes mathematicae, ISSN 0001-9054, 6/2018, Volume 92, Issue 3, pp. 497 - 513

The packing chromatic number $$\chi _{\rho }(G)$$ χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets $$V_i$$ Vi , $$i\in [k]$$ i∈[k] , where each $$V_i$$ Vi is an i...

05C12 | Packing chromatic number | Analysis | Mathematics | 05C70 | Clique number | Combinatorics | Chromatic number | Independence number | 05C15 | Mycielskian

05C12 | Packing chromatic number | Analysis | Mathematics | 05C70 | Clique number | Combinatorics | Chromatic number | Independence number | 05C15 | Mycielskian

Journal Article

Aequationes Mathematicae, ISSN 0001-9054, 02/2017, Volume 91, Issue 1, pp. 169 - 184

The packing chromatic number chi(p)(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets Pi(1),...,Pi(k), where Pi...

Packing chromatic number | Petersen graph | Generalized prism | Subdivision | S-coloring | Cubic graph | COLORINGS | MATHEMATICS | MATHEMATICS, APPLIED | HEXAGONAL LATTICE | PRODUCT | DISTANCE GRAPHS | Prisms | Graphs | Integers | Subdivisions | Texts | Formulas (mathematics) | Unions

Packing chromatic number | Petersen graph | Generalized prism | Subdivision | S-coloring | Cubic graph | COLORINGS | MATHEMATICS | MATHEMATICS, APPLIED | HEXAGONAL LATTICE | PRODUCT | DISTANCE GRAPHS | Prisms | Graphs | Integers | Subdivisions | Texts | Formulas (mathematics) | Unions

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2018, Volume 341, Issue 2, pp. 474 - 483

...≤i≤k the distance between any two distinct x,y∈Vi is at least i+1. The packing chromatic number, χp(G...

Packing coloring | Cubic graphs | Independent sets | MATHEMATICS | REGULAR GRAPHS

Packing coloring | Cubic graphs | Independent sets | MATHEMATICS | REGULAR GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2015, Volume 190-191, pp. 127 - 140

The packing chromatic number χρ(G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i+1. Goddard et al. (2008...

Packing chromatic number | Upper bound | Hypercube graphs | COLORINGS | MATHEMATICS, APPLIED | HEXAGONAL LATTICE | PRODUCT | DISTANCE GRAPHS

Packing chromatic number | Upper bound | Hypercube graphs | COLORINGS | MATHEMATICS, APPLIED | HEXAGONAL LATTICE | PRODUCT | DISTANCE GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 02/2019, Volume 255, pp. 209 - 221

Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exist subclasses in which the packing chromatic number is finite (and small...

Packing colouring | Subcubic graphs | Packing chromatic number | Outerplanar graphs | COLORINGS | MATHEMATICS, APPLIED | SQUARE | PRODUCT | LATTICE | Graphs | Lattices | Computer Science | Discrete Mathematics

Packing colouring | Subcubic graphs | Packing chromatic number | Outerplanar graphs | COLORINGS | MATHEMATICS, APPLIED | SQUARE | PRODUCT | LATTICE | Graphs | Lattices | Computer Science | Discrete Mathematics

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 7/2016, Volume 32, Issue 4, pp. 1313 - 1327

The packing chromatic number $$\chi _{\rho }(G)$$ 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...

Packing chromatic number | Packing | Mathematics | 05C70 | Engineering Design | Combinatorics | Sierpiński graphs | 05C15

Packing chromatic number | Packing | Mathematics | 05C70 | Engineering Design | Combinatorics | Sierpiński graphs | 05C15

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 1110 - 1115

The packing chromatic number χρ(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...

Packing chromatic number | Subdivision | Cubic graph | Contraction | COLORINGS | MATHEMATICS | HEXAGONAL LATTICE | PRODUCT | DISTANCE GRAPHS

Packing chromatic number | Subdivision | Cubic graph | Contraction | COLORINGS | MATHEMATICS | HEXAGONAL LATTICE | PRODUCT | DISTANCE GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2017, Volume 225, pp. 136 - 142

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...

Broadcast chromatic number | Graph colouring | Packing chromatic number | SAT solving | MATHEMATICS, APPLIED

Broadcast chromatic number | Graph colouring | Packing chromatic number | SAT solving | MATHEMATICS, APPLIED

Journal Article

Discrete Mathematics, ISSN 0012-365X, 07/2017, Volume 340, Issue 7, pp. 1645 - 1648

Inspired by Bondarenko’s counter-example to Borsuk’s conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers are significantly higher than the dimensions...

Ball packing | Generalized quadrangles | Chromatic number | Strongly regular graphs | MATHEMATICS | 2-GRAPH | CONJECTURE

Ball packing | Generalized quadrangles | Chromatic number | Strongly regular graphs | MATHEMATICS | 2-GRAPH | CONJECTURE

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 03/2019, Volume 35, Issue 2, pp. 513 - 537

.... The packing chromatic number, p(G), of a graph G is the minimum k such that G has a packing k-coloring...

Packing coloring | Cubic graphs | Independent sets | COLORINGS | MATHEMATICS | Coloring | Graphs | Subdivisions | Upper bounds

Packing coloring | Cubic graphs | Independent sets | COLORINGS | MATHEMATICS | Coloring | Graphs | Subdivisions | Upper bounds

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2012, Volume 160, Issue 4-5, pp. 518 - 524

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that vertices of G can be partitioned into disjoint classes X1...

Packing coloring | Distance graph | Packing chromatic number | MATHEMATICS, APPLIED | Integers | Lower bounds | Graphs | Gaps | Mathematical analysis

Packing coloring | Distance graph | Packing chromatic number | MATHEMATICS, APPLIED | Integers | Lower bounds | Graphs | Gaps | Mathematical analysis

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2018, Volume 341, Issue 8, pp. 2337 - 2342

Recently, Balogh et al. (2018) 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...

Coloring | Subcubic graph | Packing | Packing coloring | Diameter | COLORINGS | MATHEMATICS | DISTANCE GRAPHS | CUBIC GRAPHS

Coloring | Subcubic graph | Packing | Packing coloring | Diameter | COLORINGS | MATHEMATICS | DISTANCE GRAPHS | CUBIC GRAPHS

Journal Article

Mathematical Programming, ISSN 0025-5610, 07/2017, Volume 164, Issue 1-2, pp. 245 - 262

We prove that every h-perfect line graph and every t-perfect claw-free graph G has the integer round-up property for the chromatic number...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | LINE GRAPHS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABLE SET | ALGORITHM | PACKING | CLAW-FREE GRAPHS | Graphs | Rounding | Computation | Weighting functions

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | LINE GRAPHS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABLE SET | ALGORITHM | PACKING | CLAW-FREE GRAPHS | Graphs | Rounding | Computation | Weighting functions

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2010, Volume 158, Issue 12, pp. 1224 - 1228

... more than k . The packing chromatic number of G is the smallest integer m such that the vertex set of G can be partitioned as V 1 , V 2...

Triangular lattice | Packing chromatic number | [formula omitted]-Packing | Integer lattice | k-Packing | MATHEMATICS, APPLIED

Triangular lattice | Packing chromatic number | [formula omitted]-Packing | Integer lattice | k-Packing | MATHEMATICS, APPLIED

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 7/2015, Volume 30, Issue 1, pp. 27 - 33

.... The minimum number of colors required for a dominator coloring of $$G$$ G is called the dominator chromatic number of $$G$$ G...

Trees | Dominator coloring | Dominating set | Mathematics | Theory of Computation | Optimization | Packing set | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematical Modeling and Industrial Mathematics | Combinatorics | 05C69 | 05C15 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Algorithms

Trees | Dominator coloring | Dominating set | Mathematics | Theory of Computation | Optimization | Packing set | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematical Modeling and Industrial Mathematics | Combinatorics | 05C69 | 05C15 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Algorithms

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 11/2013, Volume 44, Issue 5, pp. 263 - 268

The packing chromatic number χρ(G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i+1. Goddard et al. [8...

packing chromatic number | upper bound | hypercube graphs | Packing chromatic number | Upper bound | Hypercube graphs | Computer Science | Discrete Mathematics

packing chromatic number | upper bound | hypercube graphs | Packing chromatic number | Upper bound | Hypercube graphs | Computer Science | Discrete Mathematics

Journal Article

Ars Mathematica Contemporanea, ISSN 1855-3966, 2015, Volume 9, Issue 2, pp. 321 - 344

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2007, Volume 155, Issue 17, pp. 2303 - 2311

The packing chromatic number χ ρ ( G ) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths...

Hexagonal lattice | Tree | Packing chromatic number | Cartesian product of graphs | Subdivision graph | Computational complexity | MATHEMATICS, APPLIED | INDEPENDENCE NUMBER | packing chromatic number | tree | subdivision graph | hexagonal lattice | computational complexity | GRAPHS | Computer science

Hexagonal lattice | Tree | Packing chromatic number | Cartesian product of graphs | Subdivision graph | Computational complexity | MATHEMATICS, APPLIED | INDEPENDENCE NUMBER | packing chromatic number | tree | subdivision graph | hexagonal lattice | computational complexity | GRAPHS | Computer science

Journal Article

Discussiones Mathematicae - Graph Theory, ISSN 1234-3099, 2012, Volume 32, Issue 4, pp. 795 - 806

.... An S-packing k-coloring of a graph G is a mapping from V(G) to {1, 2,..., k} such that vertices with color i have pairwise distance greater than a, and the S-packing chromatic number chi(s)(G...

Broadcast chromatic number | Coloring | Graph | Packing | MATHEMATICS | coloring | broadcast chromatic number | packing | graph

Broadcast chromatic number | Coloring | Graph | Packing | MATHEMATICS | coloring | broadcast chromatic number | packing | graph

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 03/2010, Volume 17, Issue 1, pp. 1 - 7

...,..., X-k, where vertices in X-i have pairwise distance greater than i. In this note we improve the upper bound on the packing chromatic number of the square lattice.

MATHEMATICS | Packing colouring | MATHEMATICS, APPLIED | Packing chromatic number | OPTIMIZATION | Square lattice

MATHEMATICS | Packing colouring | MATHEMATICS, APPLIED | Packing chromatic number | OPTIMIZATION | Square lattice

Journal Article

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