2015/08/18 by Changqing Xu, Xu, Changqing, Ziyan Luo +3 · 2 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1508.04204
arxiv created 2015/08/18 · arxiv updated 2015/08/19
Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized as a higher-order extension of matrices, the multi-hypergraph, regarded as a generalization of graphs, is then introduced to associate with tensors for the study of complete positivity. To describe the dependence of the corresponding zero pattern for a special type of completely positive tensors--the \0,1\ completely positive tensors, the completely positive multi-hypergraph is defined. By characterizing properties of the associated multi-hypergraph, we provide necessary and sufficient conditions for any (0,1) associated tensor to be \0,1\ completely positive. Furthermore, a necessary and sufficient condition for a uniform multi-hypergraph to be completely positive multi-hypergraph is proposed as well.