Random Latin square graphs

TL;DR

This paper introduces new random graph models based on Latin squares, exploring their properties and comparing them with existing models like Cayley graphs, often achieving comparable or improved results.

Contribution

It presents a novel class of random graphs derived from Latin squares, extending and enhancing the understanding of their structural properties.

Findings

Properties similar to Cayley graphs for many parameters

Results often match or surpass known Cayley graph results

Insights into expansion, connectivity, and Hamiltonicity

Abstract

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and several similarities and differences are pointed out. For many properties our results for the general case are as strong as the known results for random Cayley graphs and sometimes improve the previously best results for the Cayley case.