Oriented hypergraphs: Balanceability |
| |
Institution: | 1. Department of Mathematics, Texas State University, San Marcos, TX 78666, USA;2. The Center of Excellence for Community Health and Economic Resiliency Research, Texas State University, San Marcos, TX 78666, USA;3. Mathworks, Texas State University, San Marcos, TX 78666, USA |
| |
Abstract: | An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance. |
| |
Keywords: | Oriented hypergraph Balanced hypergraph Balanced matrix Balancing sets Signed graph |
本文献已被 ScienceDirect 等数据库收录! |
|