The largest demigenus of a bipartite signed graph

Thomas Zaslavsky
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
A graph with signed edges is orientation embedded in a surface when it is topologically embedded so that one trip around a closed path preserves or reverses orientation according as the path's sign product is positive or negative. We ÿnd the smallest surface within which it is possible to orientation-embed the complete bipartite signed graph ±Kr;s, which is obtained from the complete bipartite graph Kr;s through replacing each edge by two parallel edges, one positive and the other negative. We discuss some consequences and related problems.
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