On a Conjecture of Thomassen Concerning Subgraphs of Large Girth

Abstract

In 1983 C. Thomassen conjectured that for every k, g is an element of N there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g.

Kuhn and Osthus [2004] proved the case g=6. We give another proof for the case g=6 which is based on a result of Furedi [1983] about hypergraphs.

We also show that the analogous conjecture for directed graphs is true.

Keywords

• Thomassen conjecture
• Subgraph
• Large Girth