Lecture 6: Paper folding: overview, definitions, connectivity, 1D flat foldability, 2D map folding
Page 5: 2D map folding: simple folds, reduction to 1D subproblems, linear-time algorithm, hardness with diagonal creases or orthogonal paper
You can view the paper by Arkin, Bender, Demaine, Demaine, Mitchell, Sethia, and Skiena on 1D flat foldability and 2D map folding.
These are rough, personal lecture notes handwritten by Erik Demaine used during lecture. Their primary purpose is for reading/review by students of the class.