My currently best (lowest) known Erdös Number is (3) as shown by the following citations:

Erdös, Paul, Furedi, M., Loebl, Martin, and Sos, V. T., "Discrepancy of Trees", Scientiarum Mathematicarum Hungarica 30, 1994, 337-356 Loebl, Martin, and Greenberg, Peter, "Strong Connectivity of Polyhedral Complexes", Journal of Algebraic Combinatorics, 1996, 117-125 Nygard, Kendall E., Greenberg, Peter, Bolkan, Waverly E., and Swenson, Elizabeth J., "Generalized Assignment Methods for the Deadline Vehicle Routing Problem", Vehicle Routing: Methods and Studies, Studies in Management Science Systems, 16, North-Holland, Amsterdam, 1988 ,102-127