Factorizing the Rado graph and infinite complete graphs

Let \mathcal{F}=\{F_{\alpha}: \alpha\in \mathcal{A}\} be a family of infinite graphs, together with \Lambda. The Factorization Problem FP(\mathcal{F}, \Lambda) asks whether \mathcal{F} can be realized as a factorization of \Lambda, namely, whether there is a factorization \mathcal{G}=\{\Gamma_{\alpha}: \alpha\in \mathcal{A}\} of \Lambda such that each \Gamma_{\alpha} is a copy of F_{\alpha}. We... Show more