Elements belonging to triangles in 3-connected matroids
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- 作者：Manoel Lemos
- 关键词：Matroid ; 3-Connected matroid ; Minimally 3-connected matroid ; Triad ; Triangle
- 刊名：Discrete Mathematics
- 出版年：2006
- 出版时间：6 November 2006
- 年：2006
- 卷：306
- 期：21
- 页码：2790-2797
- 全文大小：189 K
文摘
An element e of a 3-connected matroid M is said to be superfluous provided black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4KFMMFW-9&_mathId=mml1&_user=10&_cdi=5632&_rdoc=19&_handle=V-WA-A-W-WV-MsSAYVA-UUA-U-AAZCWAYYYY-AAZWDEEZYY-VWUDVCVY-WV-U&_acct=C000050221&_version=1&_userid=10&md5=d7e53e4bac713d984e11941234f128ad"" title=""Click to view the MathML source"">M/e is 3-connected. In this paper, we show that a 3-connected matroid M with exactly k superfluous elements has at least
elements covered by triangles. For each k, an infinite family of matroids that attain this bound is constructed.