Covering Multigraphs by Simple Circuits

Answering a question raised in [SIAM J. Comput., 10 (1981), pp. 746–750], we show that every bridgeless multigraph with v vertices and e edges can be covered by simple circuits whose total length is at most $\min ( \tfrac{5}{3} e, e + \tfrac{7}{3} v - \tfrac{7}{3} )$. Our proof supplies an efficient algorithm for finding such a cover.