Towards a splitter theorem for internally 4-connected binary matroids VIII: Small matroids

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• 作者：Carolyn Chun^a ; ^{chun@usna.edu} ; Dillon Mayhew^b ; ¹ ; ^{dillon.mayhew@vuw.ac.nz} ; James Oxley^c ; ^{oxley@math.lsu.edu}
• 关键词：05B35
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：85
• 期：Complete
• 页码：12-30
• 全文大小：566 K
• 卷排序：85

文摘

Our splitter theorem studies pairs of the form (M,N)(M,N), where M and N are internally 4-connected binary matroids, M has a proper N  -minor, and if M′M′ is an internally 4-connected matroid such that M   has a proper M′M′-minor and M′M′ has an N  -minor, then |E(M)|−|E(M′)|>3|E(M)|−|E(M′)|>3. The analysis in the splitter theorem requires the constraint |E(M)|≥16|E(M)|≥16. In this article, we complement that analysis by describing all such pairs for which |E(M)|≤15|E(M)|≤15.