An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let La denote a class of all such properties. In the paper, we consider Hreducible over La properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.

We investigate which switching classes do not contain a bipartite graph. Our final aim is a characterization by means of a set of critically non-bipartite graphs: they do not have a bipartite switch, but every induced proper subgraph does. In addition to the odd cycles, we list a number of exceptional cases and prove that these are indeed critically non-bipartite. Finally, we give a number of s...

The Gram dimension gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignment of unit vectors to the nodes of the graph, there exists another assignment of unit vectors lying in R, having the same inner products on the edges of the graph. The class of graphs satisfying gd(G) ≤ k is minor closed for fixed k, so it can characterized by a finite list of forbidden minors. For k ...

Kracht formulas are first-order correspondents of modal Sahlqvist formulas. In this paper we present a model-theoretic characterization of Kracht formulas similar to Van Benthem’s theorem saying that a first-order formula is equivalent to a modal formula iff it is invariant under bisimulation. Our characterization yields a method to prove that a given first-order formula is not equivalent to an...

Electrical networks are defined and a definition of when a bond graph and an electrical network are equivalent is given. Bond graphs and electrical networks are defined to be primitive if they contain no transformers or gyrators. A bond graph is defined to be realisable if it is equivalent to an electrical network and primitively realisable if it is equivalent to a primitive electrical network....

Let H be a fixed forbidden graph and let f be a function of n: Denote by RTðn;H; f ðnÞÞ the maximum number of edges a graph G on n vertices can have without containing H as a subgraph and also without having at least f ðnÞ independent vertices. The problem of estimating RTðn;H; f ðnÞÞ is one of the central questions of so-called Ramsey–Turán theory. In their recent paper (Discrete Math. 229 (20...

Culture-based and genomics methods provide different insights into the nature and behavior of bacteria. Maximizing the usefulness of both approaches requires recognizing their limitations and employing them appropriately. Genomic analysis excels at identifying bacteria and establishing the relatedness of isolates. Culture-based methods remain necessary for detection and enumeration, to determin...

A jump system is a set of lattice points satisfying a certain “two-step” axiom. We present a variety of results concerning the geometry of these objects, including a characterization of two-dimensional jump systems, necessary (though not sufficient) properties of higher-dimensional jump systems, and a characterization of constant-sum jump systems.