On the cyclic decomposition of circulant graphs into almost-bipartite graphs.
Ryan C. Bunge, Saad I. El‐Zanati, Chepina Rumsey, Charles Vanden Eynden · Australas. J Comb. · 2011
It is known that if an almost bipartite graph G with n edges possesses a γlabeling, then the complete graphK2nx+1 admits a cyclicG-decomposition. We introduce a variation of γ-labeling and show that whenever an almost bipartite graph G admits such a labeling, then there exists a cyclic Gdecomposition of a family of circulant graphs. We also determine which odd length cycles admit the variant labeling.