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...

Control flow graphs represent the possible execution paths of a program and can be obtained by static analysis of software binaries. We give a formal characterization of the subclass of control flow graphs that correspond to structured code.

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...

PURPOSE This article makes an attempt to synthesize certain compounds containing thiazole and imidazole moieties and screen for the antimicrobial properties. METHODS The novel compounds synthesized were characterized by elemental analysis, IR and (1)HNMR spectral data. The antimicrobial activity of novel compounds was evaluated by cup plate method. RESULTS The compound p-t showed more antib...

In this paper we characterize those forbidden triples of graphs, no one of which is a generalized claw, su2cient to imply that a 2-connected graph of su2ciently large order is hamiltonian. c © 2002 Elsevier Science B.V. All rights reserved.