Determination of the 4-genus of a complete graph (with an appendix)

Serge Lawrencenko, Beifang Chen, Hui Yang

In this paper, the quadrangular genus (4-genus) of the complete graph $K_p$ is shown to be ${\gamma }_4(K_p)=\lceil p(p-5)/8\rceil +1$ for orientable surfaces. This means that $K_p…