Results 11 to 20 of about 1,143 (224)
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
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, Taolue Chen
exaly +12 more sources
Independence Number and Packing Coloring of Generalized Mycielski Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2021 For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1 ...
Bidine Ez Zobair +2 more
doaj +4 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 +13 more sources
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
doaj +3 more sources
Packing chromatic vertex-critical graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\in [k]$, where vertices in $V_i$ are pairwise at distance at least $i+1$.
Sandi Klavžar, Douglas F. Rall
doaj +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 +3 more sources
Packing chromatic number of transformation graphs [PDF]
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