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The bchromatic number of cubic graphs
 Graphs and Combinatorics
"... The bchromatic number of a graph G is the largest integer k such that G admits a proper kcoloring in which every color class contains at least one vertex adjacent to some vertex in all the other color classes. It is proved that with four exceptions, the bchromatic number of cubic graphs is 4. The ..."
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Cited by 13 (3 self)
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The bchromatic number of a graph G is the largest integer k such that G admits a proper kcoloring in which every color class contains at least one vertex adjacent to some vertex in all the other color classes. It is proved that with four exceptions, the bchromatic number of cubic graphs is 4
Packing Chromatic Number of Distance Graphs
"... 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,..., Xk where vertices in Xi have pairwise distance greater than i. We study the packing chromatic number of infinite distance graphs G(Z, D), i.e. graphs wit ..."
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Cited by 3 (1 self)
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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,..., Xk where vertices in Xi have pairwise distance greater than i. We study the packing chromatic number of infinite distance graphs G(Z, D), i.e. graphs
On the packing chromatic number of hypercubes
, 2013
"... 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] found an upper bound for the packing chromatic number of hypercubes Qn. ..."
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Cited by 1 (0 self)
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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] found an upper bound for the packing chromatic number of hypercubes Qn
ON THE PACKING CHROMATIC NUMBER ON HAMMING GRAPHS AND GENERAL GRAPHS
"... 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 the distance between any two vertices having color i be at least i + 1. We obtain χρ(Hq,m) for m = 3, where Hq,m is the Hamming graph of words of length m and alphabet wit ..."
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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 the distance between any two vertices having color i be at least i + 1. We obtain χρ(Hq,m) for m = 3, where Hq,m is the Hamming graph of words of length m and alphabet
Critical chromatic number and the complexity of perfect packings in graphs
 17th ACMSIAM Symposium on Discrete Algorithms (SODA), (2006), 851– 859. Oliver Cooley, Daniela Kühn & Deryk Osthus School of Mathematics Birmingham University Edgbaston Birmingham B15 2TT UK Email addresses: {cooleyo,kuehn,osthus}@maths.bham.ac.uk
"... Abstract. Let H be any nonbipartite graph. We determine asymptotically the minimum degree of a graph G which ensures that G has a perfect Hpacking. More precisely, we determine the smallest number τ having the following property: For every positive constant γ there exists an integer n0 = n0(γ, H) ..."
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Cited by 11 (7 self)
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Abstract. Let H be any nonbipartite graph. We determine asymptotically the minimum degree of a graph G which ensures that G has a perfect Hpacking. More precisely, we determine the smallest number τ having the following property: For every positive constant γ there exists an integer n0 = n0(γ, H
The packing chromatic number of infinite product graphs
, 2008
"... The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V (G) can be partitioned into disjoint classes X1,..., Xk, where vertices in Xi have pairwise distance greater than i. For the Cartesian product of a path and the 2dimensional square lattice it is pro ..."
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Cited by 8 (2 self)
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The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V (G) can be partitioned into disjoint classes X1,..., Xk, where vertices in Xi have pairwise distance greater than i. For the Cartesian product of a path and the 2dimensional square lattice
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