{2, 2}-Extendability of Planar Graphs
Dharmaiah Gurram, N. Vedavathi · 2014
Abstract:- In this paper, the idea of assigning lists of varying sizes to vertices of a planar graph will be explored. Thomassen’s 5-list-coloring theorem states that plane graphs are list-colorable 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 2-extendable. Thomassen also defined an analogous property of 3-extendability, and later Definition, which corresponds to having the vertices of a 3-path along the boundary of the unbounded face precolored. While every planar graph is 2-extendable, it is not the case that every planar graph is 3-extendable. Keywords:- {i, j}-extendability, {2, 2, 2}-extendable, 3-cycle. I.