
{2, 2}EXTENDABILITY OF PLANAR GRAPHSAbstract: In this paper, the idea of assigning lists of varying sizes to vertices of a planar graph will be explored. Thomassen’s 5listcoloring theorem states that plane graphs are listcolorable when two adjacent vertices on the boundary of the unbounded face are precolored, other vertices on the boundary of the unbounded face are assigned lists of size 3, and all other vertices of the graph are assigned lists of size 5. This can be thought of as being 2extendable. Thomassen’s also defined an analogous property of 3extendability, and later Definition, which corresponds to having the vertices of a 3path along the boundary of the unbounded face precolored. While every planar graph is 2extendable, it is not the case that every planar graph is 3extendable. Keywords: {i, j}extendibility, {2, 2, 2}extendable, 3cycle.
