We prove a precise characterization of toroidal graphs with no K3,3-subdivisions in terms of forbidden minors and subdivisions. The corresponding lists of four forbidden minors and eleven forbidden subdivisions are shown.

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 ...

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...

PURPOSE The aim of the study was to evaluate the effect of 3 silicone primers and 3 surface characterization of acrylic resin surface on bond strength between silicone elastomer and acrylic resin. MATERIALS AND METHODS 96 Cosmesil silicones bonded to heat-curing acrylic resin were fabricated with the dimension of 75 × 10 × 3 mm. The 3 primers used in this study were G611 platinum primer, A-33...