Immersions of bipartite graphs and numismatics

S. A. Bogatyy, S. F. Grubiyanov

Lomonosov Moscow State University (Moscow)

Abstract: Bipartite immersions of a bipartite graph into a plane with a minimum self-intersection number are studied. For some classes of bipartite graphs, the minimum self-intersection number is calculated for all bipartite immersions. In particular, all graphs with a bipartite embedding into a plane are described. Appendixes are given to the chronological ordering of the initial coinage of Shirvanshah Abu Mansur Ali bin Yazid (425-435 AH = 1034-1044 AD).

Keywords: finite-multiple mapping into Euclidean space, dimension, dense subset.

UDC: 515.163.6

Received: 15.01.2025
Accepted: 07.04.2025

DOI: 10.22405/2226-8383-2025-26-2-33-48