Grinberg's well-known necessary condition for a planar graph to be Hamiltonian was extended by Shimamoto to a condition for having a 2-factor. We derive a necessary condition for a planar graph to contain a collection of n disjoint circuits, none of which separates any other two. All is done in terms of the numbers pk which denote the numbers of k-gonal faces.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics