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...

Workload characterization is an important technique that helps us understand the performance of parallel applications and the demands they place on the system. It can be used to describe performance effects due to application parameters, compiler options, and platform configurations. In this paper, workload characterization features in the TAU parallel performance system are demonstrated for el...

We give the first linear-time certifying algorithms to recognize split graphs, threshold graphs, chain graphs, co-chain graphs and trivially perfect graphs, with sublinear certificates for negative output. In case of membership in a given graph class our algorithms provide as certificate a structure for the input graph that characterizes the class, and in case of non-membership they provide as ...

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...