The Connectivity Game

Abstract

Recall that we denote the hypergraph of the connectivity game by $\mathcal{C}\;=\;\mathcal{C}(n)\;=\;\left\{E(T)\;\subseteq\;2^{E(K_n)}\; : \; T\; \mathrm{is\; a\; spanning \;tree\; of}\;K_{n}\right\}$. We continue here where we left off in Chapter 3 and will be after the threshold bias $b_{\mathcal{C}}\;=\;b_{\mathcal{C}}(n)$ of the Maker-Breaker connectivity game.

It is through science that we prove, but through intuition that we discover.

Henri Poincaré