We discover new hereditary classes of graphs that are minimal (with respect to set inclusion) of unbounded clique-width. The new examples include split permutation graphs and bichain graphs. Each of these classes is characterised by a finite list of minimal forbidden induced subgraphs. These, therefore, disprove a conjecture due to Daligault, Rao and Thomassé from 2010 claiming that all such mi...

background toxoplasma gondii is a unicellular apicomplex organism, belonging to the toxoplasma genus. the parasite infects humans, as well as mammalians and different species of birds, and it can be propagated in a wide range of host cells. there have been no appropriate molecular or serological studies carried out previously in iran on the prevalence of toxoplasma gondii in rodents. objectives...

let $g$ be a finite group and $gamma(g)$ the prime graph of $g$‎. ‎recently people have been using prime graphs to study simple groups‎. ‎naturally we pose a question‎: ‎can we use prime graphs to study almost‎ ‎simple groups or non-simple groups? in this paper some results in‎ ‎this respect are obtained and as follows‎: ‎$gcong s_p$ if and only‎ ‎if $|g|=|s_p|$ and $gamma(g)=gamma(s_p)$‎, ‎whe...

In 1996, Ota and Tokuda showed that a star-free graph with sufficiently high minimum degree admits a 2-factor. More recently it was shown that the minimum degree condition can be significantly reduced if one also requires that the graph is not only star-free but also of sufficiently high edge-connectivity. In this paper we reduce the minimum degree condition further for star-free graphs that al...

We give a characterization, in terms of forbidden induced subgraphs, of those graphs in which every connected induced subgraph has a dominating induced path on at most k vertices (k 3). We show, in particular, that k = 4 means precisely the class of domination-reducible graphs, whose original definition applied four types of structural reduction. © 2006 Elsevier B.V. All rights reserved.

We consider flag-transitive extensions of the dual Petersen graph satisfying one of the following "pathological" properties: (-riLL) there are pairs of collinear points incident to more than one line; ( -TT) there are triples of collinear points not incident to the same plane. We prove that ihere is just one example-satisfying (~LL), with six points and $6 as its au tomorphism group, and there ...

If 9 is a collection of connected graphs, and if a graph G does not contain any member of 9 as an induced subgraph, then G is said to be F-free. The members of f in this situation are called forbidden subgraphs. In a previous paper (Gould and Harris, 1995) the authors demonstrated two families of triples of subgraphs which imply traceability when forbidden. In this paper the authors identify tw...

For a set F of connected graphs, a graph G is said to be F-free if G does not contain any member of F as an induced subgraph. The members of F are referred to as forbidden subgraphs. When we study the relationship between forbidden subgraphs and a certain graph property, we often allow the existence of exceptional graphs as long as their number is finite. However, in this type of research, if t...

Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has at most n times a polylogarithmic number of edges, where the exponent of the logarithmic factor depends on k. In the case where C consists of convex sets, we improve this bound to O(n log n). If in addition k = 2, the ...

Let S be any set of points in the Euclidean plane R2. For any p = (x, y) ∈ S, put SW (p) = {(x, y) ∈ S : x < x and y < y} and NE(p) = {(x, y) ∈ S : x > x and y > y}. Let GS be the graph with vertex set S and edge set {pq : NE(p) ∩ NE(q) 6= ∅ and SW (p) ∩ SW (q) 6= ∅}. We prove that the graphH with V (H) = {u, v, z, w, p, p1, p2, p3} and E(H) = {uv, vz, zw, wu, p1p3, p2p3, pu, pv, pz, pw, pp1, p...