Local equivalence of transversals in matroids
The electronic journal of combinatorics, Tome 3 (1996) no. 1
Given any system of $n$ subsets in a matroid $M$, a transversal of this system is an $n$-tuple of elements of $M$, one from each set, which is independent. Two transversals differing by exactly one element are adjacent, and two transversals connected by a sequence of adjacencies are locally equivalent, the distance between them being the minimum number of adjacencies in such a sequence. We give two sufficient conditions for all transversals of a set system to be locally equivalent. Also we propose a conjecture that the distance between any two locally equivalent transversals can be bounded by a function of $n$ only, and provide an example showing that such function, if it exists, must grow at least exponentially.
@article{10_37236_1248,
author = {D. Fon-Der-Flaass},
title = {Local equivalence of transversals in matroids},
journal = {The electronic journal of combinatorics},
year = {1996},
volume = {3},
number = {1},
doi = {10.37236/1248},
zbl = {0885.05048},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1248/}
}
D. Fon-Der-Flaass. Local equivalence of transversals in matroids. The electronic journal of combinatorics, Tome 3 (1996) no. 1. doi: 10.37236/1248
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