We prove a precise characterization of toroidal graphs with no K3,3-subdivisions in terms of forbidden minors and subdivisions. The corresponding lists of four forbidden minors and eleven forbidden subdivisions are shown.

We provide a doubly exponential upper bound in p on the size of forbidden pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field F of linear rank-width at most p. As a corollary, we obtain a doubly exponential upper bound in p on the size of forbidden vertex-minors for graphs of linear rank-width at most p. This solves an open question raised by Jeong, Kwon, and Oum [Ex...

Singular values and maximum rank minors of generalized inverses are studied. Proportionality of maximum rank minors is explained in terms of space equivalence. The Moore–Penrose inverse A† is characterized as the {1}–inverse of A with minimal volume.

5 Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. 6 Using this result we show that internally 4-connected projective-planar graphs are characterized 7 by 23 internally 4-connected excluded minors. 8

The classes of binary and ternary matroids are both relatively well understood as is their intersection, the class of regular matroids. This paper considers the union M of the classes of binary and ternary matroids. M is a minor-closed class and the focus of the paper is on determining its set of excluded minors. It is conjectured here that this set of excluded minors unique matroids that are o...

Electronic cigarette (EC) use is currently subject to a debate concerning safety, regulation need, and probable contribution to smoking cessation. An important gap in this debate is the lack of distinction between minors and adults. This is problematic because other principles of prevention apply to long-term users (such as most adult smokers) and experimental or probable users (more common in ...

This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ideals of minors of a given size are prime. The “generic” case, where all the entries are distinct variables has been studied extensively (cf. [1] and [2] for a thorough account.) While some special cases, such as catale...

Tobacco smoking and exposure to secondhand smoke are major environmental risk factors that negatively influence health. It is recommended that tobacco product manufacturers and retailers receive empowerment counseling programs to achieve adolescent health targets. The present study conducted an empowerment counseling session to counsel tobacco product retailers in refusing to sell tobacco produ...

Many students change their majors during college. Choosing the right academic majors, minors, and concentrations within a major in higher education is challenging but crucial in assuring students’ overall academic and career success. Personalized prediction of student success in majors, minors, and concentrations will help students better find the right majors, minors, and concentrations for th...