Acknowledgements The authors were thankful to the anonymous relerees for the meaningful suggestions to improve the paper. The first author's work was supported in part by the National Natural Science Foundation of China (Grant No. 11171180) and the second author's work was supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 502111, 501212, 501913, 15302114).
Stimulated by odd-bipartite and even-bipartite hypergraphs, we define odd-bipartite (weakly odd-bipartie) and even-bipartite (weakly even- bipartite) tensors. It is verified that all even order odd-bipartite tenso...