We prove a common generalization of two results, one on rainbow fractional matchings and one on rainbow sets in the intersection of two matroids: Given $d=r\lceil k\rceil -r+1$ functions of size (=sum of values) $k$ that are all independent in each of $r$ given matroids, there exists a rainbow set of $supp(f_i), ~i \le d$, supporting a function with the same properties.
@article{10_37236_8844,
author = {Joseph Briggs and Minki Kim},
title = {Choice functions in the intersection of matroids},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8844},
zbl = {1427.05045},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8844/}
}
TY - JOUR
AU - Joseph Briggs
AU - Minki Kim
TI - Choice functions in the intersection of matroids
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8844/
DO - 10.37236/8844
ID - 10_37236_8844
ER -
%0 Journal Article
%A Joseph Briggs
%A Minki Kim
%T Choice functions in the intersection of matroids
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8844/
%R 10.37236/8844
%F 10_37236_8844
Joseph Briggs; Minki Kim. Choice functions in the intersection of matroids. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8844
