Let IG(x, y) and JG(x, y) be the geodesic and induced path interval between x and y in a connected graph G, respectively. The following three betweenness axioms are considered for a set V and R : V × V → 2 (i) x ∈ R(u, y), y ∈ R(x, v), x 6= y, |R(u, v)| > 2 ⇒ x ∈ R(u, v) (ii) x ∈ R(u, v) ⇒ R(u, x) ∩R(x, v) = {x} (iii)x ∈ R(u, y), y ∈ R(x, v), x 6= y,⇒ x ∈ R(u, v). We characterize the class of g...

A class of graphs is Kruskalian if Kruskal’s theorem on a well-quasi-ordering of finite trees provides a finite characterization in terms of forbidden induced subgraphs. Let k be a natural number. A graph is a k-cograph if its vertices can be colored with colors from the set {1, . . . ,k} such that for every nontrivial subset of vertices W there exists a partition {W1,W2} of W into nonempty sub...

A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing one of the vertices of a magnet together with all edges linking the other one to its proper neighbours without changing the stability number. We characterize a class of graphs such that by repeated use ...

A graph G is coordinated if, for every induced subgraph H of G, the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques of H with a common vertex. In a previous work, coordinated graphs were characterized by minimal forbidden induced subgraphs within some ...

The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e1; : : : ; er) in such a way that for every i = 1; : : : ; r 1, there are at most k vertices incident to edges that belong both to fe1; : : : ; eig and to fei+1; : : : ; erg. In this paper, we give a set of 57 graphs and prove that it is the set of the minimal for...

For a hereditary property P let kP(G) denote the number of forbidden subgraphs contained in G. A graph G is said to be weakly Psaturated, if G has the property P and there is a sequence of edges of G, say e1, e2, . . . , el, such that the chain of graphs G = G0 ⊂ G0+e1 ⊂ G1 + e2 ⊂ . . . ⊂ Gl−1 + el = Gl = Kn (Gi+1 = Gi + ei+1) has the following property: kP(Gi+1) > kP(Gi), 0 ≤ i ≤ l − 1. In thi...

abstract background: fascioliasis, caused by fasciola hepatica and f. gigantica , has medical and economic importance in the world. molecular approaches comparing tradi­tional methods using for identification and characterization of fasciola spp. are precise and reliable. the aims of current study were molecular characterization of fasciola spp. in west azerbaijan province, iran and then compar...

Chordal graphs, also called triangulated graphs, are important in algorithmic graph theory. In this paper we generalise the definition of chordal graphs to the class of directed graphs. Several structural properties of chordal graphs that are crucial for algorithmic applications carry over to the directed setting, including notions like simplicial vertices, perfect elimination orderings, and ch...

AgraphG is a k-leaf power if there is a tree T such that the vertices ofG are the leaves of T and two vertices are adjacent in G if and only if their distance in T is at most k. In this situation T is called a k-leaf root of G. Motivated by the search for underlying phylogenetic trees, the notion of a k-leaf power was introduced and studied by Nishimura, Ragde and Thilikos and subsequently in v...