1. Prove, disprove (give a counterexample, highlight the incorrectness or give the correct answer) or complete a proof. (1) Let f be a face of a planar drawing of a graph H, and let u1,..., Un be a subsequence of vertices in the boundary walk off. Let f' be a face of a planar drawing of a graph J, and let W1,..., w, be a subsequence of vertices in the boundary walk of f'. Then the property that the amalgamated graph (HU J)/{U1=W1,..., Un=wn} is planar does not hold for n > 3. Definition: Let W be a set of vertices in a graph G and x another vertex not in W. A strict X-W path is a path joining vertex x to a vertex in W and containing no other vertex of W. A strict W-x path is the reverse of a strict x-W path