Document Type
Lecture
Publication Date
1-14-2009
Abstract
Let M be a matroid with rank function r, and let e E(M). The deletion-contraction polymatroid with rank function f = rMe +rM e will be denoted Pe(M). The polymatroid Pe(M) is uniquely determined by M and e. Similarly, a deletion-contraction polymatroid determines M, unless e is a loop or coloop. This talk will characterize all polymatroids of this deletioncontraction form by giving the set of excluded minors. Vertigan conjectured that the class of GF(q)- representable deletion-contraction polymatroids is well-quasi- ordered. From this attractive conjecture, both Rotas Conjecture and the WQO Conjecture for GF(q)-representable matroids would follow.
Relational Format
presentation
Recommended Citation
Chun, Deborah, "Deletion-Contraction Polynomials" (2009). Combinatorics Seminar. 85.
https://egrove.olemiss.edu/math_combinatorics/85
