The minimum number of over/underpasses that are needed to draw a graph with no edge crossings is its genus.

Because K5 is not planar, it cannot be drawn in the plane without any edge crossings. However, if an over/underpass is erected on the plane, it is then possible to draw K5 with no edge crossings. (See the figure.) The minimum number of over/underpasses that are needed to draw a graph with no edge crossings is its genus. Thus, planar graphs have genus 0 and K5 has genus 1. The genus for K6 is _________.

0Comment