We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...

We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...

In this paper we compute explicit formulas for the commutation relations between any two quantum minors in the quantum matrix bialgebraOq (Mn(k)). The product of any two minors is expressed as linear combination of products of minors strictly less in certain orderings.  2004 Elsevier Inc. All rights reserved.

OBJECTIVE To estimate the effect on cigarette sales rates when minors present identification (ID). DESIGN Controlled experiment in which minors attempting to purchase cigarettes either carried a valid photo ID (documenting they were minors) or carried no ID, and were instructed to show the ID or admit having no ID if the clerk requested proof of age. SETTING Census of retail stores in six u...

n Many studies reported a decline in minors’ abortion rate associated with parental involvement laws. However, most of these studies did not measure abortions among minors who leave the state, or stop coming into the state, because of the law. Studies in Mississippi and Massachusetts, which incorporated data on minors traveling out of state, found no effect on the abortion rate, while one in Te...

BACKGROUND Selling of tobacco products to minors has been banned since 1996 by the tobacco control law in Turkey. However, it is also important for the public to support practices that prevent the access of tobacco products to minors. In addition, every individual has the responsibility of carrying out society based programs that restrict access to tobacco products especially to children and th...

Minors are a special group with immature heart and in the growing stage, whose rights interests more vulnerable to infringement of Internet information world. For minors, it is necessary take consideration design protection rules law. Different types personal will be distinguished, combined specific application situation, further distinguish age consent matters, maximize balance between relativ...

Research on adjustment of internationally adopted children indicates that, although they have adequate development, more emotional and behavioral problems are detected compared with nonadopted children. In this research, emotional and behavioral characteristics of a sample of 52 internationally adopted minors were examined with the BASC (Parent Rating Scales and Self-Report of Personality), com...

We show that for pairs and of disjoint subsets vertices a graph , if is sufficiently large, then there exists vertex in such are two ways to reduce by vertex-minor operation removes while preserving the connectivity between . Our theorem implies an analogous Chen Whittle (SIAM J. Discrete Math., 28 (2014), pp. 1402--1404) matroids restricted binary matroids.

For every integer t there is a smallest real number c(t) such that any graph with average degree at least c(t) must contain a Kt-minor (proved by Mader). Improving on results of Shapira and Sudakov, we prove the conjecture of Fiorini, Joret, Theis and Wood that any graph with n vertices and average degree at least c(t) + ε must contain a Kt-minor consisting of at most C(ε, t) logn vertices. Mad...