Host-plant acceptance on mineral soil and humus by the pine weevil Hylobius abietis (L.)

1 The pine weevil Hylobius abietis (L.) (Coleoptera, Curculionidae) is an economically important pest of conifer forest regeneration in Europe and Asia. 2 Soil scarification, which usually exposes mineral soil, is widely used to protect seedlings from weevil attack. However, the mechanism behind this protective effect is not yet fully understood. 3 Field experiments were conducted to determine the pine weevil's responses to visual and odour stimuli from seedlings when moving on mineral soil and on undisturbed humus surface. 4 One experiment measured the number of pine weevils approaching seedlings, with and without added host odour, on mineral soil and undisturbed humus. Seedlings with added host odour attracted more weevils on both soil types. Unexpectedly, somewhat more weevils approached seedlings surrounded by mineral soil. 5 In a similar experiment, feeding attacks on seedlings planted directly in the soil were recorded. Only half as many seedlings were attacked on mineral soil as on undisturbed humus. 6 In the first experiment, the weevils were trapped 2.5 cm from the bases of the seedlings' stems, whereas they could reach the seedlings in the experiment where seedlings were planted directly in the soil. We conclude that the pine weevils' decision on whether or not to feed on a seedling is strongly influenced by the surrounding soil type and that this decision is taken in the close vicinity of the seedling. The presence of pure mineral soil around the seedling strongly reduces the likelihood that an approaching pine weevil will feed on it

New Graph Classes of Bounded Clique-Width

Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ1,L ) by Courcelle, Makowsky and Rotics, is linear-time solvable on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time. The notion of clique-width..

Bandwidth on AT-free graphs

We study the classical Bandwidth problem from the viewpoint of parameterized algorithms. In the Bandwidth problem we are given a graph G = (V, E) together with a positive integer k, and asked whether there is an bijective function β: {1,..., n} → V such that for every edge uv ∈ E, |β −1 (u) − β −1 (v) | ≤ k. The problem is notoriously hard, and it is known to be NP-complete even on very restricted subclasses of trees. The best known algorithm for Bandwidth for small values of k is the celebrated algorithm by Saxe [SIAM Journal on Algebraic and Discrete Methods, 1980], which runs in time 2 O(k) n k+1. In a seminal paper, Bodlaender, Fellows and Hallet [STOC 1994] ruled out the existence of an algorithm with running time of the form f(k)n O(1) for any function f even for trees, unless the entire W-hierarchy collapses. We initiate the search for classes of graphs where Bandwidth is fixed parameter tractable (FPT), that is, solvable in time f(k)n O(1) for some function f. In this paper we present an algorithm with running time 2 O(k log k) n 2 for Bandwidth on AT-free graphs, a well-studied graph class that contains interval, permutation, and cocomparability graphs. Our result is the first non-trivial FPT algorithm for Bandwidth on a graph class where the problem remains NP-complete

Confluent Drawings: Visualizing Non-planar Diagrams in a Planar Way

We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing non-planar graphs in a planar way. This approach allows us to draw, in a crossing-free manner, graph - such as software interaction diagrams - that would normally have many crossings. The main idea of this approach is quite simple: we allow groups of edges to be merged together and drawn as "tracks" (similar to train tracks). Producing such confluent diagrams automatically from a graph with many crossings is quite challenging, however, so we offer two heuristic algorithms to test if a non-planar graph can be drawn efficiently in a confluent way. In addition, we identify several large classes of graphs that can be completely categorized as being either confluently drawable or confluently non-drawable

Computing graph polynomials on graphs of bounded clique-width

Abstract. We discuss the complexity of computing various graph polynomials of graphs of fixed clique-width. We show that the chromatic polynomial, the matching polynomial and the two-variable interlace polynomial of a graph G of clique-width at most k with n vertices can be computed in time O(n f(k)), where f(k) ≤ 3 for the inerlace polynomial, f(k) ≤ 2k + 1 for the matching polynomial and f(k) ≤ 3 · 2 k+2 for the chromatic polynomial.