Special case of Rota’s basis conjecture on graphic matroids

Shun Ichi Maezawa, Akiko Yazawa

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article numberP3.63
JournalElectronic Journal of Combinatorics
Volume29
Issue number3
DOIs
Publication statusPublished - 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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