Finding a small 3-connected minor maintaining a fixed minor and a fixed element |
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Authors: | Robert E Bixby C R Coullard |
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Institution: | (1) Dept. Math. Sci, Brown School Eng., P.O.B. 1892, 77251-1892 Houston, Tx, USA;(2) School of Industrial Engineering Grissom Hall, Purdue University, 47907 West Lafayette, IN, USA |
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Abstract: | LetN andM be 3-connected matroids, whereN is a minor ofM on at least 4 elements, and lete be an element ofM and not ofN. Then, there exists a 3-connected minor \(\bar M\) ofM that usese, hasN as a minor, and has at most 4 elements more thanN. This result generalizes a theorem of Truemper and can be used to prove Seymour’s 2-roundedness theorem, as well as a result of Oxley on triples in nonbinary matroids. |
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Keywords: | 05 B 35 |
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