An n × n matrix is called an N 0-matrix if all its specified principal minors are nonpositive. In the context of partial matrices, a partial matrix is called a partial N 0-matrix if all its specified principal minors are nonpositive. In this paper we characterize the existence of an N 0-matrix completion of a partial N 0-matrix whose associated graph is a directed cycle.

The thickness problem on graphs is NP-hard and only few results concerning this graph invariant are known. Using a decomposition theorem of Truemper, we show that the thickness of the class of graphs without G 12-minors is less than or equal to two (and therefore, the same is true for the more well-known class of the graphs without K 5-minors). Consequently, the thickness of this class of graph...

We prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to M∗(K3,k), M(Wk), M(Kk), the cycle matroid of the graph obtained from K2,k by adding paths through the vertices of each vertex class, or the cycle matroid of the graph obtained from K3,k by adding a complete graph on the vertex class with three vertices.

The majority of adolescent smokers are able to purchase cigarettes even though laws prohibit the sale of cigarettes to minors (Radecki & Zdunich, 1993). The present study focused on merchant licensing, civil penalties, and monitoring of merchant behavior. Several different schedules of enforcement in the city of Chicago were evaluated to determine the optimal schedules to reduce the sale of cig...

Exclusion of minor, vertex-minor, induced subgraph Tree-structuring Monadic second-order logic : expression of properties, queries, optimization functions, number of configurations. Mainly useful for tree-structured graphs (Second-order logic useless) Tools to be presented Algebraic setting for tree-structuring of graphs Recognizability = finite congruence ≡ inductive computability ≡ finite det...