Hajós-like theorem for signed graphs

The paper designs five graph operations, and proves that every signed graph with chromatic number q, defined by Kang and Steffen (in press), can be obtained from copies of the all-positive complete graph (Kq,+) by repeatedly applying these operations. This result gives a signed version of the Hajós theorem, emphasizing the role of all-positive complete graphs in the class of signed graphs, as in the class of unsigned graphs. Moreover, a similar result is established for the signed chromatic number defined by Máčajová, Raspaud and Å koviera.