
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 th...
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EntropyBased Proofs of Combinatorial Results on Bipartite Graphs
This work considers new entropybased proofs of some known, or otherwise...
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Observability Properties of Colored Graphs
A colored graph is a directed graph in which either nodes or edges have ...
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Maximum Matchings and Minimum Blocking Sets in Ξ_6Graphs
Ξ_6Graphs are important geometric graphs that have many applications es...
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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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On the Difficulty of Selecting Ising Models with Approximate Recovery
In this paper, we consider the problem of estimating the underlying grap...
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Formalizing Graph Trail Properties in Isabelle/HOL
We describe a dataset expressing and proving properties of graph trails,...
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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 colorings of a graph G. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on π(G) and prove that these conjectures are true for specific classes of graphs such as triangulated graphs and graphs with maximum degree at most 2.
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