[PDF][PDF] A survey on packing colorings

B Brešar, J Ferme, S Klavžar… - Discussiones …, 2020 - bibliotekanauki.pl
If S=(a1, a2,...) is a non-decreasing sequence of positive integers, then an S-packing
coloring of a graph G is a partition of V (G) into sets X1, X2,... such that for each pair of …

[HTML][HTML] Modeling the packing coloring problem of graphs

Z Shao, A Vesel - Applied Mathematical Modelling, 2015 - Elsevier
The frequency assignment problem asks for assigning frequencies to transmitters in a
wireless network and includes a variety of specific subproblems. In particular, the packing …

[HTML][HTML] A note on S-packing colorings of lattices

W Goddard, H Xu - Discrete Applied Mathematics, 2014 - Elsevier
Abstract Let a 1, a 2,…, ak be positive integers. An (a 1, a 2,…, ak)-packing coloring of a
graph G is a mapping from V (G) to {1, 2,…, k} such that vertices with color i have pairwise …

[HTML][HTML] The packing coloring of distance graphs D (k, t)

J Ekstein, P Holub, O Togni - Discrete Applied Mathematics, 2014 - Elsevier
The packing chromatic number χ ρ (G) of a graph G is the smallest integer p such that
vertices of G can be partitioned into disjoint classes X 1,…, X p where vertices in X i have …

Packing chromatic number of base-3 Sierpiński graphs

B Brešar, S Klavžar, DF Rall - Graphs and Combinatorics, 2016 - Springer
The packing chromatic number χ _ ρ (G) χ ρ (G) of a graph G is the smallest integer k such
that there exists ak-vertex coloring of G in which any two vertices receiving color i are at …

Packing coloring of some undirected and oriented coronae graphs

L Daouya, I Bouchemakh, É Sopena - arXiv preprint arXiv:1506.07248, 2015 - arxiv.org
The packing chromatic number $\pcn (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 $ V\_1 $,\ldots …

Packing Coloring of Undirected and Oriented Generalized Theta Graphs

D Laïche, I Bouchemakh, É Sopena - arXiv preprint arXiv:1606.01107, 2016 - arxiv.org
The packing chromatic number $\chi $$\rho $(G) of an undirected (resp. oriented) graph G is
the smallest integer k such that its set of vertices V (G) can be partitioned into k disjoint …

Packing chromatic number of certain fan and wheel related graphs

S Roy - AKCE International Journal of Graphs and …, 2017 - Taylor & Francis
The packing chromatic number χ ρ (G) of a graph G is the smallest integer k for which there
exists a mapping π: V (G)⟶{1, 2,…, k} such that any two vertices of color i are at distance at …

On the packing chromatic number of Moore graphs

J Fresán-Figueroa, D González-Moreno… - Discrete Applied …, 2021 - Elsevier
The packing chromatic number χ ρ (G) of a graph G is the smallest integer k for which there
exists a vertex coloring Γ: V (G)→{1, 2,…, k} such that any two vertices of color i are at …

On S-packing colourings of distance graphs D (1, t) and D (1, 2, t)

P Holub, J Hofman - Applied Mathematics and Computation, 2023 - Elsevier
For a non-decreasing sequence of positive integers S=(s 1, s 2,…), the S-packing chromatic
number χ S (G) of a graph G is the smallest integer k such that the vertex set of G can be …