The Eigenvalue Method for Extremal Problems on Infinite Vertex-Transitive Graphs

This thesis is about maximum independent set and chromatic number problems on certain kinds of infinite graphs. A typical example comes from the Witsenhausen problem: For $n \geq 2$, let $S^{n-1} := \{ x \in \R^n : \|x\|_2 =1 \}$ be the unit sphere in $\R^n$, and let $G=(V,E)$ be the graph with $V = S^{n-1}$, in which two points in $S^{n-1}$ are...