Structure theorem and algorithm on [formula omitted]-odd subgraph

Abstract

The authors give a Gallai–Edmonds type structure theorem on ( 1 , f ) -odd subgraphs and a polynomial algorithm for finding an optimal ( 1 , f ) -odd subgraph. Lovász [The factorization of graphs. II. Acta Math. Acad. Sci. Hungar. 23 (1972) 223–246] and Cornuéjols [General factors of graphs, J. Combin. Theory Ser. B 45(2) (1988) 185–198] solved these problems for a more general problem, the general factor problem with gaps at most 1. However, the statements of the theorems and the algorithm are much more simple in this special case, so it is worth of interest on its own. Also, the algorithm given for this case is faster than the general algorithm. The proofs follow a direct approach instead of deducing from the general case.