2015/10/09 by Rong Chen, Chen, Rong, Zifei Gao +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Graph theory and applications #math.CO
paper · pdf · doi:10.48550/arxiv.1510.02643
openalex publication_date 2015/10/09 · arxiv created 2016/07/03 · arxiv updated 2016/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph G, the circuits of its bicircular lift matroid are the edge sets of those subgraphs of G 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 2-isomorphic in the sense of Whitney.