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Title: Graphs of Homomorphisms

Abstract: If X and Y are graphs and f is a function on V (X) taking values in V (Y ), then the graph of
f is the subset formed by the pairs (x; f(x)) for x in V (X).

Title: Extending Thomassen’s Theorem to Two Faces

Abstract:

Let G be a planar graph and let L be a list-assignment for G in which there is a precolored edge on the outer face, every other vertex on the outer face has a list of size at least 3, and every other vertex in G has a list of size at least 5.