Large cycles in random generalized Johnson graphs

TL;DR

This paper investigates the conditions under which large cycles of varying lengths appear in random generalized Johnson graphs, providing threshold values for different growth scenarios.

Contribution

It establishes thresholds for the emergence of large cycles in random generalized Johnson graphs, advancing understanding of their structural properties.

Findings

Thresholds identified for large cycle existence

Growth rates influence cycle thresholds

Results applicable to graph theory and network analysis

Abstract

This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.