We consider the problem of permutation reconstruction, which is a variant of graph reconstruction. Given a permutation p of length n, we delete k of its entries in each possible way to obtain (n k ) subsequences. We renumber the sequences from 1 to n−k preserving the relative size of the elements to form (n−k)-minors. These minors form a multiset Mk(p) with an underlying set M ′ k(p). We study ...

CONTEXT Prior research on the effect of laws mandating parental involvement in minors' abortions has failed to examine an important behavioral response to such laws: Older teenagers may delay an abortion until age 18; for some, this may mean terminating a pregnancy after the first trimester. METHODS Statewide data were obtained on abortions in Texas in 1997-2003. Analysis of relative rate rat...

we give a new recursive method to compute the number of cliques and cycles of a graph. this method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. in particular, let $g$ be a graph and let $overline {g}$ be its complement, then given the chromatic polynomial of...

We say a digraph G is a minor of a digraph H if G can be obtained from a subdigraph of H by repeatedly contracting a strongly-connected subdigraph to a vertex. Here, we show the class of all tournaments is a well-quasi-order under minor containment.

For a given graph G and integers b, f ≥ 0, let S be a subset of vertices of G of size b + 1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most n/ b+f b such vertex subsets. This result from extremal combinatorics appears to be very useful in the design of several e...

BACKGROUND Recent large clinical trials have found that pre-exposure prophylaxis (PrEP) reduced HIV infection among men who have sex with men (MSM), but efforts to provide clinical care to minors, including young MSM, may be complicated by a lack of clarity regarding parental consent requirements with respect to medical services. PURPOSE The goal of this paper was to analyze law related to a ...

The class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: K4 and K2,3. The class of graphs that contain a vertex whose removal leaves an outerplanar graph is also minor-closed. We provide the complete list of 57 excluded minors for this class.

Introduction In many states, minors can get abortions, treatment for sexually transmitted diseases, or mental health services without their parents’ knowledge or consent. In the era of electronic health information exchange, however, maintain­ ing this confidentiality is a vexing challenge. Information about minors is subject to myriad laws that require health care providers to treat it differe...

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M(G1), . . . ,M(G29), R15, R16. Here G1, . . . , G29 are the vertically 2-connected excluded minors for the class of projective-planar graphs.

For adolescents under the age of 18, holding a job is a beneficial experience, not only for the income, but also for the discipline, education, and skills acquired. although no accurate statistics are available that describe the actual numbers of adolescent workers, the US Bureau of Labor Statistics estimated that at least 4 million minors were legally registered as employees in the country in ...