I'm asking this because there are very similar theroems describing these properties: A lattice is distributive if and only if it does not contain N5 (pentagon) or M3 (diamond) and according to Kuratowski's theorem, a graph is planar if and only if it does not contain a subgraph which is homeomorphic to K5 or K3,3. Can these forbidden sublattices/subgraphs be somehow paired? Is there any reason why these theorems look so similar?
Thank you in advance!