Speaker
Description
A signed graph is a pair $(G,\Sigma)$ where $G$ is a graph and $\Sigma$ is a subset of edges of $G$. We say that a cycle $C$ of $G$ is even in $(G,\Sigma)$ if $|C \cap \Sigma|$ is even; otherwise, $C$ is odd. A matroid $M$ is an even-cycle matroid if there exists a signed graph $(G,\Sigma)$ such that the circuits of $M$ precisely correspond to the even cycles or the unions of two odd cycles sharing at most one vertex. Isomorphism problem for even-cycle matroids is the problem of characterizing two signed graphs $(G_1,\Sigma_1)$ and $(G_2, \Sigma_2)$ representing the same even-cycle matroid. In this talk, I will give the structures for solving this problem when $G_1$ and $G_2$ are $4$-connected.
This is joint work with Bertrand Guenin and Irene Pivotto.
