Guessing Numbers and Extremal Graph Theory

For a given number of colors, $s$, the guessing graph is (base $s$) logarithm cardinality largest family colorings vertex set such that color each can be determined from colors vertices in its neighborhood. This quantity related to problems network coding, circuit complexity and entropy. We study graphs as property context classic extremal questions, relationship forbidden subgraph property. find with respect having $\leq a$, for fixed $a$. Furthermore, we an upper bound on saturation this property, method construct further saturated lie between these two extremes. show that, bounding equivalent forbidding finite subgraphs.