Cayley partitionable graphs and near-factorizations of finite groups Original Research Article

In this paper, we investigate the class of Cayley partitionable graphs. This investigation is motivated by the Strong Perfect Graph Conjecture. Cayley partitionable graphs are Cayley graphs which are closely related to near-factorizations of finite groups. We prove that near-factorizations satisfy a strong structural property. We used it to speed up exhaustive computations, which revealed a Cayley partitionable graph with 50 vertices, which is not generated by all constructions of partitionable graphs known so far.