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DeCorte, P.E.B. (author)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...doctoral thesis 2015