\input zb-basic \input zb-ioport \iteman{io-port 01347062} \itemau{Reed, Bruce} \itemti{Edge coloring nearly bipartite graphs.} \itemso{Oper. Res. Lett. 24, No. 1-2, 11-14 (1999).} \itemab Summary: We give a simple polynomial time algorithm to compute the chromatic index of graphs which can be made bipartite by deleting a vertex. An analysis of this algorithm shows that for such graphs, the chromatic index is the roundup of the fractional chromatic index. \itemrv{~} \itemcc{} \itemut{} \itemli{doi:10.1016/S0167-6377(98)00041-8} \end