Title: Extending Thomassen’s Theorem to Two Faces
|Affiliation:||University of Waterloo|
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. Thomassen’s celebrated theorem then states that G is L-colorable. It is natural to ask if this theorem can be extended to two faces whose vertices have lists of size 3, provided that these two faces are sufficiently far part. Postle and Thomas developed a far-reaching set of results which they used to show that there exists a constant D>0 for which this holds even for arbitrarily many faces pairwise of distance at least D apart. In this talk, we review these results and techniques and show how to use them to extend Thomassen’s Theorem to two faces of at least constant distance apart.
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