TITLE: Is there a polynomial-time algorithm to check if a signed graph contains an odd-K5 minor?
QUESTION [5 upvotes]: I suspect this exists, if anyone has a reference please that would be very helpful.
By signed graph, I mean each edge is designated either odd or even (e.g. as in Guenin's result for weakly bipartite graphs).

REPLY [11 votes]: Yes.  This result is contained in my PhD thesis, which is available here (see Theorem 1.1.10).  We prove that for any finite abelian group $\Gamma$ and fixed $\Gamma$-labeled graph $H$, there is a polynomial time algorithm to determine if an input $\Gamma$-labelled graph $G$ contains an $H$-minor.  The case you are interested in is $\Gamma=\mathbb{Z} / 2 \mathbb{Z}$ and $H$ equals odd-$K_5$.  For signed graphs, this result was also obtained independently by Kawarabayashi, Reed, and Wollan (although I am not sure that a journal version is available yet).