Restrictions On Smallest Counterexamples To The 5-Flow Conjecture

Using counting arguments, we show that every smallest counterexample to Tutte’s 5-flow Conjecture (that every bridgeless graph has a nowhere-zero 5-flow) has girth at least 9. * This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-027604 and partially by VEGA grant 2/4004/04. The author was also affiliated at the School of Mathematics, Georgia Institute of Technology, the Department of Mathematics, Vanderbilt University.