On the Decomposition of Vertex-Transitive Graphs into Multicycles
نویسنده
چکیده
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 cam be expressed as the edge-disjoint union of multicycles. We verify this conjecture for several subclasses of vertextransitive 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.
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