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...

We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.

A permutation is said to be –avoiding if it does not contain any subsequence having all the same pairwise comparisons as . This paper concerns the characterization and enumeration of permutations which avoid a set of subsequences increasing both in number and in length at the same time. Let be the set of subsequences of the form “ ”, being any permutation on . For ! the only subsequence in #" i...

We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. © 2015 Elsevier B.V. All rights reserved.

In the study of full bubble model graphs of bounded clique-width and bounded linear clique-width, we determined complete sets of forbidden induced subgraphs, that are minimal in the class of full bubble model graphs. In this note, we show that (almost all of) these graphs are minimal in the class of all graphs. As a corollary, we can give sets of minimal forbidden induced subgraphs for graphs o...

Forbidden minors and subdivisions for toroidal graphs are numerous. In contrast, the toroidal graphs with no K3,3’s have a nice explicit structure and short lists of obstructions. For these graphs, we provide the complete lists of four forbidden minors and eleven forbidden subdivisions.

A graph is 1-extendible if every edge has a 1-factor containing it. A 1-extendible non-bipartite graph G is said to be near bipartite if there exist edges e1 and e2 such that G − {e1, e2} is 1-extendible and bipartite. We characterise the Pfaffian near bipartite graphs in terms of forbidden subgraphs. The theorem extends an earlier characterisation of Pfaffian bipartite graphs.