In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of K3,n in a surface with Euler genus ε is

The crossing number of Sierpiński graphs S(n, k) and their regularizations S(n, k) and S(n, k) is studied. Explicit drawings of these graphs are presented and proved to be optimal for S(n, k) and S(n, k) for every n ≥ 1 and k ≥ 1. These are the first nontrivial families of graphs of “fractal” type whose crossing number is known.

In 1958, Hill conjectured that the minimum number of crossings in a drawing of Kn is exactly Z(n) = 1 4 ⌊n 2 ⌋ ⌊