On factorisations of complete graphs into circulant graphs and the Oberwolfach Problem

TL;DR

This paper investigates how complete graphs can be decomposed into circulant graphs and applies these findings to solve instances of the Oberwolfach Problem, especially for specific prime-related cases.

Contribution

It provides new factorisation results of complete graphs into circulant graphs and offers a complete solution to the Oberwolfach Problem for certain 2-regular graphs.

Findings

Complete solutions to the Oberwolfach Problem for 2-regular graphs of order 2p with p ≡ 5 (mod 8) prime.

New factorisation methods for complete graphs into circulant graphs.

Enhanced understanding of 2-factorisations of circulant graphs.

Abstract

Various results on factorisations of complete graphs into circulant graphs and on 2-factorisations of these circulant graphs are proved. As a consequence, a number of new results on the Oberwolfach Problem are obtained. For example, a complete solution to the Oberwolfach Problem is given for every 2-regular graph of order 2p where p = 5 (mod 8) is prime.