Signed analogs of bipartite graphs

Thomas Zaslavsky Binghamton University Binghamton, New York, U.S.A. 13902-6000 September 1991 Revised July 1996 Abstra t We hara terize the edge-signed graphs in whi h every \signi ant" positive losed walk (or ombination of walks) has even length, under seven di erent riteria for signi an e, and also those edge-signed graphs whose double overing graph is bipartite. If the property of even length is generalized to positivity in a se ond edge signing, the hara terizations generalize as well. We also hara terize the edge-signed graphs with the smallest nontrivial hromati numbers. Resear h and preparation of this report were supported by the SGPNR under grant 9009BCW747 and by the NSF under grant DMS-9200472. Many thanks to the referee for helping me make this paper readable.