Calculating Crossing Numbers of Graphs Using Combinatorial Principles

Abstract

The crossing numbers of graphs were started from Turán’s brick factory problem (TBFP). Because of its wide range of applications, it has been used in computer networks, electrical circuits, and biological engineering. Recently, many experts began to pay much attention to the crossing number of G \ e , which obtained from graph G by deleting an edge e . In this paper, by using some combinatorial skills, we determine the exact value of crossing numbers of K 1,4 , n \ e and K 2,3 , n \ e . These results are an in-depth work of TBFP, which will be beneficial to the further study of crossing numbers and its applications.