Extremal bipartite subgraphs of cubic triangle-free graphs

A cubic triangle-free graph has a bipartite subgraph with at least 4/5 of the original edges. Examples show that this is a best possible result. It is easy to verify that the Petersen graph may be reduced to a bipartite graph by the removal of three of its 15 edges, and that this may not be done by the removal of two edges. Similarly, the Dodecahedron graph… CONTINUE READING