On the Decomposition of Vertex-Transitive Graphs into Multicycles

In this paper, we prove that every vertex-transitive graph can be expressed as the edge-disjoint union of symmetric graphs. We define a multicycle graph and conjecture that every vertex-transitive graph can be expressed as the edge-disjoint union of multicycles. We verify this conjecture for several subclasses of vertex-transitive graphs, including Cayley graphs, multidimensional circulants, and vertex-transitive graphs with a prime or twice a prime number of nodes. We conclude with some open questions of interest.