| Reductions of Connected Simple $r$-Uniform Hypergraphs |
| Received:September 11, 2013 Revised:October 10, 2014 |
| Key Words:
graph families reductions uniform hypergraphs
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| Fund Project:Supported by NRF South Africa and the National Natural Science Foundation of China (Grant No.11161032). |
| Author Name | Affiliation | | Sheng BAU | School of Mathematics, University of the Witwatersrand, Johannesbury, South Africa
Institute of Discrete Mathematics, Inner Mongolia University of Nationalities, Inner Mongolia 028005, P. R. China | | Jirimutu | Institute of Discrete Mathematics, Inner Mongolia University of Nationalities, Inner Mongolia 028005, P. R. China | | Changchang YIN | Center for Discrete Mathematics, Fuzhou University, Fujian 350002, P. R. China |
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| Abstract: |
| It is proved in this paper that if $G$ is a simple connected $r$-uniform hypergraph with $\|G\|\geq 2$, then $G$ has an edge $e$ such that $G - e - V_1(e)$ is also a simple connected $r$-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple $r$-uniform hypergraphs are also determined. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.01.002 |
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