The paper considers the problem of learning classes of graphs closed under taking minors It is shown that any such class can be properly learned in polynomial time using membership and equivalence queries The representation of the class is in terms of a set of minimal excluded minors obstruction set

The number of excluded minors for the graphs with path-width at most two is too large. To give a practical characterization of the obstructions for path-width at most two, we introduce the concept reducibility. We describe some operations, which preserve path-width at most two, and reduce the excluded minors to smaller graphs. In this sense, there are ten graphs which are non-reducible and obst...

We introduce a notion of bipartite minors and prove a bipartite analog of Wagner’s theorem: a bipartite graph is planar if and only if it does not contain K3,3 as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite (2, 2)-Laman graphs — a certain family of graphs that contains...

The paper considers the problem of learning classes of graphs closed under taking minors. It is shown that any such class can be properly learned in polynomial time using membership and equivalence queries. The representation of the class is in terms of a set of minimal excluded minors (obstruction set). Moreover, a negative result for learning such classes using only equivalence queries is als...

We show that for each permutation w containing no decreasing subsequence of length k, the Kazhdan-Lusztig immanant Immw(x) vanishes on all matrices having k equal rows or columns. Also, we define two filtrations of the vector space of immanants via products of matrix minors and pattern avoidance and use the above result to show that these filtrations are equivalent. Finally, we construct new an...

The relevance of the problem under study lies in fact that criminal liability juvenile criminals is one most difficult areas law. Minors, given their physiological, mental, and social characteristics, are considered a separate category criminals, being vulnerable segments population. Therefore, delinquency manifests itself not only causing harm to public relations, personality victim, but also ...

We prove an upper bound on sums of squares of minors of {+1, −1}-matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [‘(1, −1)-matrices with near-extremal properties’, SIAM J. Discrete Math. 23 (2009), 1422–1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices. 2010 Mathematics subject classification: primary 05B...

In this article we introduce a full-rank representation of the Drazin inverse AD of a given complex matrix A, which is based on an arbitrary full-rank decomposition of Al, l ≥ k, where k is the index of A. We show that the known representation of the Drazin inverse of A, devised in [7], represents a partial case of this result. Using this general representation, we introduce a determinantal rep...

In a recent publication, the lack of consensus among U.S. laws regarding the age at which minors may consent to confidential treatment for abuse of illegal substances was highlighted. This article reports the results of an investigation of the information used by legislators to determine the age at which minors may consent to treatment. Evidence indicates that in four states lawmakers considere...