Crossing numbers of periodic graphs

TL;DR

This paper proves that the limit crossing number of a periodic graph, constructed by cyclically joining identical components, is a computable value, resolving a question posed in 2004.

Contribution

It establishes the computability of the limit crossing number for periodic graphs, a previously open problem in graph theory.

Findings

Limit crossing number of periodic graphs is computable.

Answers a longstanding open question from 2004.

Provides a method to determine crossing numbers for cyclic graph constructions.

Abstract

A graph is periodic if it can be obtained by joining identical pieces in a cyclic fashion. It is shown that the limit crossing number of a periodic graph is computable. This answers a question of Benny Pinontoan and Bruce Richter (2004).