English

Representations of bicircular lift matroids

Combinatorics 2016-07-05 v2

Abstract

Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph GG, the circuits of its bicircular lift matroid are the edge sets of those subgraphs of GG that contain at least two cycles, and are minimal with respect to this property. The main result of this paper is a characterization of when two graphs give rise to the same bicircular lift matoid, which answers a question proposed by Irene Pivotto. In particular, aside from some appropriately defined "small" graphs, two graphs have the same bicircular lift matroid if and only if they are 22-isomorphic in the sense of Whitney.

Keywords

Cite

@article{arxiv.1510.02643,
  title  = {Representations of bicircular lift matroids},
  author = {Rong Chen and Zifei Gao},
  journal= {arXiv preprint arXiv:1510.02643},
  year   = {2016}
}
R2 v1 2026-06-22T11:16:31.248Z