KöMaL 2014 A606

Prove that for every simple graph $G$ with $n$ vertices there exist some simple graphs $S_1$, ..., $S_k$ with the following properties: ($a$) every $S_i$ is a complete bipartite graph; ($b$) every edge of $G$ is contained by an odd number of graphs $S_i$; ($c$) every edge of the complement of $G$ is contained by an even number of graphs $S_i$; ($d$) $k\le\frac34n$ .