Circuit decompositions of join-covered graphs

In this paper, we focus our attention on join-covered graphs, that is, ±1-weighted graphs, without negative circuits, in which every edge lies in a zero-weight circuit. Join covered graphs are a natural generalization of matching-covered graphs. Many important properties of matching covered graphs, such as the existence of a canonical partition, tight cut decomposition and ear decomposition, have been generalized to join covered graphs by A. Sebo [5]. In this paper we prove that any two edges of a join-covered graph lie on a zero-weight circuit (under an equivalent weighting), generalize this statement to an arbitrary number of edges, and characterize minimal bipartite join-covered graphs. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 220–233, 2009 The work was done during C. H. C. Little's visit to UFMS, Brazil, in 2006.