Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices.

We characterize graphs that have intersection representations using unit intervals with open or closed ends such that all ends of the intervals are integral in terms of infinitely many minimal forbidden induced subgraphs. Furthermore, we provide a quadratic-time algorithm that decides if a given interval graph admits such an intersection representation.

An undirected graph G = (V, E) is a probe split graph if its vertex set can be partitioned into two sets, N (nonprobes) and P (probes) where N is independent and there exists E′ ⊆ N ×N such that G′ = (V, E ∪ E′) is a split graph. Recently Chang et al. gave an O(V (V +E)) time recognition algorithm for probe split graphs. In this article we give O(V 2 +V E) time recognition algorithms and charac...

A method for recognition of Persian handwritten digits based on characterization loci and mixture of experts is proposed. This method utilizes the characterization loci, as the main feature. In the classification stage of our proposed method the mixture of experts are applied. This recognition method is applied to Farsi hand-written digits in the HODA database. The experimental results support ...

Recently Postnikov gave a combinatorial description of the cells in a totallynonnegative Grassmannian. These cells correspond to a special class of matroids called positroids. We prove his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a combinatorial description of positroids that is easily computable. The main proof is purely combinatorial,...

We show that the norm graph constructed in [13] with n vertices about 1 2n 2−1/t edges, which contains no copy of Kt,(t−1)!+1, does not contain a copy of Kt+1,(t−1)!−1.

In this paper we investigate the closure ~-* under substitution-composition of a family of graphs ~,, defined by a set Lr of forbidden configurations. We first prove that ~-* can be defined by a set L~* of forbidden subgraphs. Next, using a counterexample we show that ~* is not necessarily a finite set, even when .~ is finite. We then give a sufficient condition for ~* to be finite and a simple...

Logical structures for modeling agents’ reasoning about unawareness are presented where it can hold simultaneously that: (i) agents’ beliefs about whether they are fully aware need not be veracious with partitional information; and (ii) the agent is fully aware if and only if she is aware of a fixed domain of formulae. In light of (ii), all states are deemed “possible”. Semantics operate in two...

We characterise t-perfect plane triangulations by forbidden induced subgraphs. As a consequence, we obtain that a plane triangulation is h-perfect if and only if it is perfect.

A circle graph is the intersection graph of a family of chords on a circle. There is no known characterization of circle graphs by forbidden induced subgraphs that do not involve the notions of local equivalence or pivoting operations. We characterize circle graphs by a list of minimal forbidden induced subgraphs when the graph belongs to one of the following classes: linear domino graphs, P4-t...