
A Brookslike result for graph powers
Coloring a graph G consists in finding an assignment of colors c: V(G)β{...
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Lower Bounds and properties for the average number of colors in the nonequivalent colorings of a graph
We study the average number π(G) of colors in the nonequivalent colorin...
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Using Graph Theory to Derive Inequalities for the Bell Numbers
The Bell numbers count the number of different ways to partition a set o...
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Simultaneous Embedding of Colored Graphs
A set of colored graphs are compatible, if for every color i, the number...
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Treedepth Bounds in Linear Colorings
Lowtreedepth colorings are an important tool for algorithms that exploi...
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Pebble Exchange Group of Graphs
A graph puzzle Puz(G) of a graph G is defined as follows. A configurati...
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Impatient PPSZ β a Faster algorithm for CSP
PPSZ is the fastest known algorithm for (d,k)CSP problems, for most val...
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Upper bounds on the average number of colors in the nonequivalent colorings of a graph
A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let π(G) be the average number of colors in the nonequivalent colorings of a graph G. We give a general upper bound on π(G) that is valid for all graphs G and a more precise one for graphs G of order n and maximum degree Ξ(G)β{1,2,n2}.
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