On the Crossing Number of Complete Graphs with an Uncrossed Hamiltonian Cycle

TL;DR

This paper establishes new lower bounds on the crossing number of complete graphs under the condition that they contain a Hamiltonian cycle without crossings, advancing understanding of graph drawing complexities.

Contribution

It provides novel lower bounds on crossing numbers for complete graphs with an uncrossed Hamiltonian cycle, a previously unexplored configuration.

Findings

New lower bounds on crossing numbers established

Conditions for Hamiltonian cycles without crossings analyzed

Implications for graph drawing complexity discussed

Abstract

We prove new lower bounds on the crossing number of a complete graphs assuming that it is drawn in such a way that it contains a Hamiltonian cycle with no crossings.