Title:
An online version of Rota's Basis Conjecture
Abstract:
In this talk, I will present the results of my graduation
project for Industrial and Applied Mathematics. Rota's Basis
Conjecture claims that, whenever there are n bases of an
n-dimensional vector space, there are n disjoint transversals
of these bases that are also bases. An analogous conjecture
exists for rank n matroids. Some background on this conjecture,
as well as a (stronger) online version of this conjecture
will be discussed. For the special case of graphic matroids,
a combinatorial algorithm will be discussed that solves the
problem for at least n up to 4.