On cocircuit covers of bicircular matroids

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• 作者：Jennifer McNulty ; Nancy Ann Neudauer
• 关键词：Matroid ; Bicircular ; Cocircuit
• 刊名：Discrete Mathematics
• 出版年：2008
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：6 September 2008
• 卷：308
• 期：17
• 页码：4008-4013
• 文件大小：160 K

摘要

Given a graph G, one can define a matroid on the edges E of G with circuits where e883aaf59efd6fd55890e12dbfb4dff"> is either the cycles of e88b91d7bbb649c936f" title="Click to view the MathML source" alt="Click to view the MathML source">G or the bicycles of 11ef493a98c5f992193632388" title="Click to view the MathML source" alt="Click to view the MathML source">G. The former is called the cycle matroid of G and the latter the bicircular matroid of G. For each bicircular matroid B(G), we find a cocircuit cover of size at most the circumference of B(G) that contains every edge at least twice. This extends the result of Neumann-Lara, Rivera-Campo and Urrutia for graphic matroids.