Maximum bipartite subgraphs of cubic triangle-free planar graphs

Abstract

Thomassen recently proved, using the Tutte cycle technique, that if G is a 3-connected cubic triangle-free planar graph then G contains a bipartite subgraph with at least 29 | V ( G ) | 24 − 7 6 edges, improving the previously known lower bound 6 | V ( G ) | 5 . We extend Thomassen’s technique and further improve this lower bound to 39 | V ( G ) | 32 − 9 16 .