Abstract:For a given number of colors, s, the guessing number of a graph is the (base s) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the colors of the vertices in its neighborhood. This quantity is related to problems in network coding, circuit complexity and graph entropy. We study the guessing number of graphs as a graph property in the context of classic extremal questions, and its relationship to the forbidd… Show more
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