Gian-Carlo Rota conjectured that for any $n$ bases $B_1,B_2,\ldots,B_n$ in a matroid of rank $n$, there exist $n$ disjoint transversal bases of $B_1,B_2,\ldots,B_n$. The conjecture for graphic matroids corresponds to the problem of an edge-decomposition as follows; If an edge-colored connected multigraph $G$ has $n-1$ colors and the graph induced by the edges colored with $c$ is a spanning tree for each color $c$, then $G$ has $n-1$ mutually edge-disjoint rainbow spanning trees. In this paper, we prove that edge-colored graphs where the edges colored with $c$ induce a spanning star for each color $c$ can be decomposed into rainbow spanning trees.
@article{10_37236_10835,
author = {Shun-ichi Maezawa and Akiko Yazawa},
title = {Special case of {Rota's} basis conjecture on graphic matroids},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10835},
zbl = {1498.05225},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10835/}
}
TY - JOUR
AU - Shun-ichi Maezawa
AU - Akiko Yazawa
TI - Special case of Rota's basis conjecture on graphic matroids
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10835/
DO - 10.37236/10835
ID - 10_37236_10835
ER -
%0 Journal Article
%A Shun-ichi Maezawa
%A Akiko Yazawa
%T Special case of Rota's basis conjecture on graphic matroids
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10835/
%R 10.37236/10835
%F 10_37236_10835
Shun-ichi Maezawa; Akiko Yazawa. Special case of Rota's basis conjecture on graphic matroids. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10835
