TY - JOUR
T1 - Special case of Rota’s basis conjecture on graphic matroids
AU - Maezawa, Shun Ichi
AU - Yazawa, Akiko
N1 - Funding Information:
Supported by JSPS KAKENHI Grant Number JP22K13956, JP20J15332, and JP20H05795.The authors would like to thank the referees for their valuable comments and suggestions. The authors would like to thank Kenta Ozeki. The first author is supported by JSPS KAKENHI Grant Number JP22K13956, JP20J15332, and JP20H05795.
Funding Information:
∗Supported by JSPS KAKENHI Grant Number JP22K13956, JP20J15332, and JP20H05795.
Funding Information:
KAKENHI Grant Number JP22K13956, JP20J15332, and JP20H05795.
Publisher Copyright:
© The authors.
PY - 2022
Y1 - 2022
N2 - Gian-Carlo Rota conjectured that for any n bases B1, B2, …, Bn in a matroid of rank n, there exist n disjoint transversal bases of B1, B2, …, Bn. The conjecture for graphic matroids corresponds to the problem of an edge-decomposition as follows; If an n-vertex 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.
AB - Gian-Carlo Rota conjectured that for any n bases B1, B2, …, Bn in a matroid of rank n, there exist n disjoint transversal bases of B1, B2, …, Bn. The conjecture for graphic matroids corresponds to the problem of an edge-decomposition as follows; If an n-vertex 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.
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U2 - 10.37236/10835
DO - 10.37236/10835
M3 - Article
AN - SCOPUS:85138324131
SN - 1077-8926
VL - 29
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 3
M1 - P3.63
ER -