The characterization of strongly perfect graphs by a restricted list of forbidden induced subgraphs has remained an open question for a long time. The minimal strongly imperfect graphs which are simultaneous imperfect are only odd holes and odd antiholes ( E. Olaru, [9]), but the entire list is not known, in spite of a lot of particular results in this direction. In this paper we give some new ...

Let L3 be the class of edge intersection graphs of linear 3-uniform hypergraphs. The problem of recognizing G ∈ L3 is NP-complete. Denote by δALG the minimal integer such that the problem ”G ∈ L3 ” is polynomially solvable in the class of graphs G with the minimal vertex degree δ(G) ≥ δALG and by δFIS the minimal integer such that L3 can be characterized by a finite list of forbidden induced su...

Antibody use is ubiquitous in the biomedical sciences. However, determining best research practices has not been trivial. Many commercially available antibodies and antibody-conjugates are poorly characterized and lack proper validation. Uncritical application of such useless tools has contributed to the reproducibility crisis in biomedical research. Despite early initiatives such as MIAPAR or ...

Graph class C is induced-hereditary if for every graph G in C, every induced subgraph of G belongs to C. Induced-hereditary graph classes allow characterisation by sets of forbidden induced subgraphs. Such characterisations are very useful for automatic deduction of relations between graph classes. However, sometimes those sets of forbidden induced subgraphs are infinite, what makes it difficul...

Silver nanoparticles (AgNPs) show different physical and chemical properties compared to their macroscale analogs. This is primarily due to their small size and, consequently, the exceptional surface area of these materials. Presently, advances in the synthesis, stabilization, and production of AgNPs have fostered a new generation of commercial products and intensified scientific investigation ...

Daligault, Rao and Thomassé asked whether a hereditary class of graphs well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this is not true for classes defined by infinitely many forbidden induced subgraphs. However, in the case of finitely many forbidden induced subgraphs the question remains open and we conjecture that ...

In this article, we present a characterization of basic graphs in terms of forbidden induced subgraphs. This class of graphs was introduced by Conforti, Cornuéjols and Vušković [3], and it plays an essential role in the announced proof of the Strong Perfect Graph Conjecture by Chudnovsky, Robertson, Seymour and Thomas [2]. Then we apply the Reducing Pseudopath Method [13] to characterize the su...

Engineered biological circuits are often disturbed by a variety of environmental factors. In batch culture, where the majority of synthetic circuit characterization occurs, environmental conditions vary as the culture matures. Turbidostats are powerful characterization tools that provide static culture environments; however, they are often expensive, especially when purchased in custom configur...

Daligault, Rao and Thomassé asked whether every hereditary graph class that is well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev (JCTB 2017+) gave a negative answer to this question, but their counterexample is a class that can only be characterised by infinitely many forbidden induced subgraphs. This raises the issue of whether the questio...

Abstract Our main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs. We conclude by exploring how some of these results over the finite field of order 2 extend to arbitrary fields and demonstrate that at least one third of the 62 ar...