Forbidden minors and subdivisions for toroidal graphs are numerous. In contrast, the toroidal graphs with no K3,3’s have a nice explicit structure and short lists of obstructions. For these graphs, we provide the complete lists of four forbidden minors and eleven forbidden subdivisions.

A graph is 1-extendible if every edge has a 1-factor containing it. A 1-extendible non-bipartite graph G is said to be near bipartite if there exist edges e1 and e2 such that G − {e1, e2} is 1-extendible and bipartite. We characterise the Pfaffian near bipartite graphs in terms of forbidden subgraphs. The theorem extends an earlier characterisation of Pfaffian bipartite graphs.

We analyze the structure of reduced expressions in the Coxeter groups An, Bn and Dn. Several special classes of elements are singled out for their connections with symmetric functions or the theory of P -partitions. Membership in these special classes is characterized in a variety of ways, including forbidden patterns, forbidden subwords, and by the form of canonically chosen reduced words.

We introduce and study a class of simplicial complexes, the orphan complexes, associated to simple graphs whose family of (open or closed) vertex-neighborhoods are anti-Sperner. Under suitable restrictions, we show that orphan complexes of such graphs are always shellable and provide a characterization of graphs in terms of induced forbidden subgraphs contained in this restricted subfamily.

In this paper we demonstrate that several theorems from [1] and [3] do not hold as they are stated. These are the theorems regarding forbidden subposet characterizations of certain classes of coverincomparability graphs. In this paper we correct a mistake in the main theorem of [1], reformulate the corresponding statements and present corrected proofs. We further characterize posets whose cover...

Flow Theory is a rich, effective theory introduced in order to study real-time network protocols. It is based on discrete mathematics in which a flow of data is represented by an infinite sequence of numbers and is characterized by its upper bounds. Unfortunately up to now Flow Theory has used a traffic characterization that in some cases can be too loose, thus causing an inefficient network ut...

From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear m...

background: acute promyelocytic leukemia (apl) is a subclass of acute myeloid leukemia. the chromosomal aberration in 95% of apl cases is t(15; 17) (q22; q21), which prevents cell differentiation. characterization of the underlying molecular lesion is valuable in determining optimal treatment strategy. the goal of this study was to develop a new and powerful flow- fish technique to detect the l...