Plane triangulations are 6-partitionable Original Research Article

Given a graph G=(V,E) and k positive integers n1,n2,…,nk such that ∑i=1k ni=|V|, we wish to find a partition P1,P2,…,Pk of the vertex set V such that |Pi|=ni and Pi induces a connected subgraph of G for all i, 1⩽i⩽k. Such a partition is called a k-partition of G. A graph G with n vertices is said to be k-partitionable if there exists a k-partition of G for any partition of n into k parts. Lovász (Acta Math. Acad. Sci. Hungar. 30 (1977) 241) showed that k-connected graphs are k-partitionable. In this paper we prove that plane triangulations are 6-partitionable. This result is the best possible as there exist plane triangulations which are not 7-partitionable.