On Bicircular Quartics with Collinear Foci

Rational Points on Quartics

Recognizing Hidden Bicircular Networks

Shull, R., A. Shuchat, J.B. Orlin and M. Lepp, Recognizing hidden bicircular networks, Discrete Applied Mathematics 41 (1993) 13-53. In this and a subsequent paper (by R. Shull, A. Shuchat, J.B. Orlin and M. Lepp), we introduce a polynomial-time algorithm for transforming an m x n matrix A by projective equivalence into the generalized incidence matrix of a bicircular generalized network N when...

Representations of bicircular matroids

Coullard, C.R., J.G. de1 Greco and D.K. Wagner, Representations of bicircular matroids, Discrete Applied Mathematics 32 (1991) 223-240. A bicircular matroid is a matroid defined on the edge set of a graph. Two different graphs can have the same bicircular matroid. The first result of this paper is a characterization of the collection of graphs having the same bicircular matroid as a given arbit...

On the equivalence of binary quartics

We give an extension and correction to a result stated in the first author’s paper Classical Invariants and 2-descent on elliptic curves, J. Symb. Comp. 31 (2001), concerning the equivalence of binary quartics. In the earlier version the cases where I = 0 or J = 0 were not fully treated, and neither were the cases of reducible quartics or those whose resolvent cubic is reducible; these are deal...

On semidefinite representations of plane quartics

This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex hull of a plane quartic to be exactly semidefinite representable with at most 12 lifting variables. If the quartic is rationally parametrizable, an exact se...