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Distant Vertex Partitions of Graphs
Combinatorics, Probability and Computing, 1998We consider the function χ(Gk), defined to be the smallest number of colours that can colour a graph G in such a way that no vertices of distance at most k receive the same colour. In particular we shall look at how small a value this function can take in terms of the order and diameter of G. We get general bounds for this and tight bounds for
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2010
Many difficult optimization problems on graphs become tractable when restricted to some classes of graphs, usually to hereditary classes. A large part of these problems can be expressed in the vertex partitioning formalism, i.e., by partitioning of the vertex set of a given graph into subsets \({V }_{1},\ldots,\!{V }_{k}\) called colour classes ...
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Many difficult optimization problems on graphs become tractable when restricted to some classes of graphs, usually to hereditary classes. A large part of these problems can be expressed in the vertex partitioning formalism, i.e., by partitioning of the vertex set of a given graph into subsets \({V }_{1},\ldots,\!{V }_{k}\) called colour classes ...
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