Nowhere-zero 3-flows in matroid base graph

作     者：Yinghao ZHANG Guizhen LIU 

作者机构：School of Mathematics Shandong University Jinan 250100 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2013年第8卷第1期

页      面：217-227页

核心收录：

学科分类：0710[理学-生物学] 1007[医学-药学(可授医学、理学学位)] 100705[医学-微生物与生化药学] 07[理学] 070104[理学-应用数学] 071005[理学-微生物学] 0701[理学-数学] 10[医学] 

基　　金：国家自然科学基金 

主　　题：Matroid base graph nowhere-zero 3-flow Z3-connectivity 

摘      要：The base graph of a simple matroid M = （E, A） is the graph G such that V（G） = A and E（G） = {BB＇： B, B＇ B, [B ／ B＇｜ = 1}, where the same notation is used for the vertices of G and the bases of M. It is proved that the base graph G of connected simple matroid M is Z3-connected if ｜V（G）｜ ≥5. We also proved that if M is not a connected simple matroid, then the base graph G of M does not admit a nowhere-zero 3-flow if and only if IV（G）[ =4. Furthermore, if for every connected component Ei （ i≥ 2） of M, the matroid base graph Gi of Mi=MIEi has IV（Gi）｜≥5, then G is Z3-connected which also implies that G admits nowhere-zero 3-flow immediately.