On Weakly Negative Subcategories, Weight Structures, and (Weakly) Approximable Triangulated Categories

Generating weakly triangulated graphs

We show that a graph is weakly triangulated, or weakly chordal, if and only if it can be generated by starting with a graph with no edges, and repeatedly adding an edge, so that the new edge is not the middle edge of any chordless path with four vertices. This is a corollary of results due to Sritharan and Spinrad, and Hayward, Hoo ang and Maaray, and a natural analogue of a theorem due to Fulk...

Triangulated and Weakly Triangulated Graphs: Simpliciality in Vertices and Edges

Recognizing Weakly Triangulated Graphs by Edge Separability

We apply Lekkerkerker and Boland's recognition algorithm for tri-angulated graphs to the class of weakly triangulated graphs. This yields a new characterization of weakly triangulated graphs, as well as a new O(m 2) recognition algorithm which, unlike the previous ones, is not based on the notion of a 2-pair, but rather on the structural properties of the minimal separators of the graph. It als...

On weakly e*-open and weakly e*-closed Functions

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

Weakly Mal’tsev Categories and Strong Relations

We define a strong relation in a category C to be a span which is “orthogonal” to the class of jointly epimorphic pairs of morphisms. Under the presence of finite limits, a strong relation is simply a strong monomorphism R → X × Y . We show that a category C with pullbacks and equalizers is a weakly Mal’tsev category if and only if every reflexive strong relation in C is an equivalence relation...