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This article contains detailed proofs and additional examples related to theUAI-2013 submission `Learning Sparse Causal Models is not NP-hard'. Itdescribes the FCI+ algorithm: a method for sound and complete causal modeldiscovery in the presence of latent confounders and/or selection bias, that hasworst case polynomial complexity of order $N^{2(k+1)}$ in the number ofindependence tests, for sparse graphs over $N$ nodes, bounded by node degree$k$. The algorithm is an adaptation of the well-known FCI algorithm by (Spirteset al., 2000) that is also sound and complete, but has worst case complexityexponential in $N$.

Proof Supplement - Learning Sparse Causal Models is not NP-hard (UAI2013)