Reductions of Connected Simple r-Uniform Hypergraphs  

作　　者：Sheng BAU Jirimutu Changchang YIN 

机构地区：[1]School of Mathematics, University of the Witwatersrand, Johannesbury, South Africa [2]Institute of Discrete Mathematics, Inner Mongolia University of Nationalities [3]Center for Discrete Mathematics, Fuzhou University

出　　处：《Journal of Mathematical Research with Applications》2015年第1期11-18,共8页数学研究及应用（英文版）

基　　金：Supported by NRF South Africa;the National Natural Science Foundation of China(Grant No.11161032)

摘　　要：It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（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.It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（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.

关 键 词：graph families REDUCTIONS uniform hypergraphs 

分 类 号：O157.5[理学—数学]