On the complexity of some colorful problems parameterized by treewidth

In this paper,we study the complexity of several coloring problems on graphs, parameterizedby the treewidth of the graph.1. The List Coloring problem takes as input a graph G, togetherwith an assignment to each vertex v of a set of colors Cv. The problem is to determinewhether it is possible to choose a color for vertex v from the set of permitted colors Cv, for each vertex, so that the obtained coloring of G is proper. We show that this problem is W[1]-hard, parameterized by the treewidth of G. The closely related Precoloring Extension problem is also shown to be W[1]-hard, parameterized by treewidth.2. An equitable coloring of a graph G is a proper coloring of the verticeswhere the numbers of vertices having any two distinct colors differs by at most one.We show that the problem is hard forW[1], parameterized by the treewidth plus the number of colors.We also show that a list-based variation, List Equitable Coloring is W[1]-hard for forests, parameterizedby the number of colors on the lists.3. The list chromatic number χl(G) of a graph G is defined to be the smallest positive integer r, such that for every assignment to the vertices v of G, of a list Lv of colors, where each list has length at least r, there is a choice of one color fromeach vertex list Lv yielding a proper coloring of G. We show that the problem of determining whether χl(G) ≤ r, the ListChromatic Number problem, is solvable in linear time on graphs of constant treewidth

Impacts of water level on metabolism and transient storage in vegetated lowland rivers: insights from a mesocosm study

Transient storage zones for water represent potential hot spots for metabolic activity in streams. In lowland rivers, the high abundance of submerged vegetation can increase water transient storage, bioreactive surface areas and, ultimately, in-stream metabolic activity. Changes in flow resulting from climatic and anthropogenic factors that influence the presence of aquatic vegetation can also, thereby, impact in-stream metabolism and nutrient cycling. We investigated the effects of water column depth on aquatic vegetation cover and its implications on water transient storage and associated metabolic activity in stream mesocosms (n=8) that represent typical conditions of lowland streams. Continuous injections of metabolically reactive (resazurin-resorufin) tracers were conducted and used to quantify hydraulic transport and whole-mesocosm aerobic respiration. Acetate, a labile carbon source, was added during a second stage of the tracer injection to investigate metabolic responses. We observed both higher vegetation coverage and resazurin uptake velocity, used as a proxy of mesocosm respiration, with increasing water column depth. The acetate injection had a slight, positive effect on metabolic activity. A hydrodynamic model estimated the water transport and retention characteristics and first-order reactivity for three mesocosms. These results suggest that both the vegetated surface water and sediments contribute to metabolically active transient storage within the mesocosms, with vegetation having a greater influence on ecosystem respiration. Our findings suggest that climate and external factors that affect flow and submerged vegetation of lowland rivers will result in changes in stream respiration dynamics and that submerged vegetation are a particularly important and sensitive location for stream respiration

Writing in Britain and Ireland, c. 400 to c. 800

No abstract available

Scandinavian Personal Names in Foreign Fields

Fellows-Jensen Gillian. Scandinavian Personal Names in Foreign Fields. In: Cahier des Annales de Normandie n°23, 1990. Recueil d'études en hommage à Lucien Musset. pp. 149-159