We study the graphs G for which the hull number h(G) and the geodetic number g(G) with respect to P3-convexity coincide. These two parameters correspond to the minimum cardinality of a set U of vertices of G such that the simple expansion process that iteratively adds to U , all vertices outside of U that have two neighbors in U , produces the whole vertex set of G either eventually or after on...

This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids M have the property that the element splitting operation, by every pair of elements on M yields a graphic matroid. This problem is solve...

Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H1, H2)-free graphs that have bounded clique-width. We also show the implications of our results for the computational complexity of the Colouring problem restricted to (H1,H2)-free grap...

In this paper we deal with a Turán-type problem: given a positive integer n and a forbidden graph H , how many edges can there be in a graph on n vertices without a subgraph H? How does a graph look like if it has this extremal edge number? The forbidden graph in this article is a clique-path: a path of length k where each edge is extended to an r-clique, r ≥ 3. We determine both the extremal n...

A finite metric is h − embeddable if it can be embedded isometrically in the N -cube (hypercube) for some N . It is known that the problem of testing whether a metric is h − embeddable is NP-Complete, even if the distances are restricted to the set {2, 4, 6 }. Here we study the problem where the distances are restricted to the set {1, 2, 3 } and give a polynomial time algorithm and forbidden su...

We study the linear clique-width of graphs that are obtained from paths by disjoint union and adding true twins. We show that these graphs have linear clique-width at most 4, and we give a complete characterisation of their linear clique-width by forbidden induced subgraphs. As a consequence, we obtain a linear-time algorithm for computing the linear clique-width of the considered graphs. Our r...

A connected edge-colored graph G is rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors; the rainbow connection number rc(G) of G is the minimum number of colors such that G is rainbow-connected. We consider families F of connected graphs for which there is a constant kF such that, for every connected F-free graph G, rc(G) ≤ diam...

reservoir characterization plays an important role in different parts of an industrial project. the results from a reservoir characterization study give insight into rock and fluid properties which can optimize the choice of drilling locations and reduce risk and uncertainty. delineating hydrocarbon bearing zones within a reservoir is the main objective of any seismic reservoir characterization...

greimas and other semioticians of the paris school believe that reality is always illusive and that the factors affecting the formation of a narrative are always ambiguous. based on this view, a narrative is always a simulation of reality. based on greimas' actants model, this paper presents an analysis of two stories from tarikh-e beyhaghi, with the aim of revealing two types of narratives; th...