Because most large, terrestrial mammalian predators have already been lost from more than 95-99% of the contiguous United States and Mexico, many ecological communities are either missing dominant selective forces or have new ones dependent upon humans. Such large-scale manipulations of a key element of most ecosystems offer unique opportunities to investigate how the loss of large carnivores affects communities, including the extent, if any, of interactions at different trophic levels. Here, we demonstrate a cascade of ecological events that were triggered by the local extinction of grizzly bears (Ursus arctos) and wolves (Canis lupus) from the southern Greater Yellowstone Ecosystem. These include (1) the demographic eruption of a large, semi-obligate, riparian-dependent herbivore, the moose (Alces alces), during the past 150 yr; (2) the subsequent alteration of riparian vegetation structure and density by ungulate herbivory; and (3) the coincident reduction of avian neotropical migrants in the impacted willow communities. We contrasted three sites matched hydrologically and ecologically in Grand Teton National Park, Wyoming, USA, where grizzly bears and wolves had been eliminated 60-75 yr ago and moose densities were about five times higher, with those on national forest lands outside the park, where predation by the two large carnivores has been replaced by human hunting and moose densities were lower. Avian species richness and nesting density varied inversely with moose abundance, and two riparian specialists, Gray Catbirds (Dumetella carolinensis) and MacGillivray's Warblers (Oporornis tolmiei), were absent from Park riparian systems where moose densities were high. Our findings not only offer empirical support for the top-down effect of large carnivores in terrestrial communities, but also provide a scientific rationale for restoration options to conserve biological diversity. To predict future impacts, whether overt or subtle, of past management, and to restore biodiversity, more must be known about ecological interactions, including the role of large carnivores. Restoration options with respect to the system that we studied in the southern Greater Yellowstone Ecosystem are simple: (1) do nothing and accept the erosion of biological diversity, (2) replace natural carnivores with human predation, or (3) allow continued dispersal of grizzly bears and wolves into previously occupied, but now vacant, habitat. Although additional science is required to further our understanding of this and other terrestrial systems, a larger conservation challenge remains: to develop public support for ecologically rational conservation options.

2008) 'Connectedness of the graph of vertex-colourings.', Discrete mathematics., 308 (5-6). pp. 913-919. Further information on publisher's website: http://dx. Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractFor a positive integer k and a graph G, the k-colour graph of G, C k (G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k-colourings are joined by an edge in C k (G) if they differ in colour on just one vertex of G. In this note some results on the connectivity of C k (G) are proved. In particular it is shown that if G has chromatic number k ∈ {2, 3}, then C k (G) is not connected. On the other hand, for k ≥ 4 there are graphs with chromatic number k for which C k (G) is not connected, and there are k-chromatic graphs for which C k (G) is connected.

Given a 3-colorable graph G together with two proper vertex 3-colorings and of G, consider the following question: is it possible to transform into by recoloring vertices of G one at a time, making sure that all intermediate colorings are proper 3-colorings? We prove that this question is answerable in polynomial time. We do so by characterizing the instances G, , where the transformation is possible; the proof of this characterization is via an algorithm that either finds a sequence of recolorings between and , or exhibits a structure which proves that no such

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. For a positive integer k, a k-colouring of a graph G = (V, E) is a mapping c : V → {1, 2, . . . , k} such that c(u) = c(v) whenever uv ∈ E. The COLOURING problem is to decide, for a given G and k, whether a k-colouring of G exists. If k is fixed (that is, it is not part of the input), we have the decision problem k-COLOURING instead. We survey known results on the computational complexity of COLOURING and k-COLOURING for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial colouring, or where lists of permissible colours are given for each vertex. Finally, we also survey results for graph classes defined by some other forbidden pattern.

A k-colouring of a graph G = (V, E) is a mapping c : V → {1, 2, . . . , k} such that c(u) = c(v) whenever uv is an edge. The reconfiguration graph of the k-colourings of G contains as its vertex set the k-colourings of G, and two colourings are joined by an edge if they differ in colour on just one vertex of G. We introduce a class of k-colourable graphs, which we call k-colour-dense graphs. We show that for each k-colour-dense graph G, the reconfiguration graph of the ℓ-colourings of G is connected and has diameter O(|V | 2 ), for all ℓ ≥ k + 1. We show that this graph class contains the k-colourable chordal graphs and that it contains all chordal bipartite graphs when k = 2. Moreover, we prove that for each k ≥ 2 there is a k-colourable chordal graph G whose reconfiguration graph of the (k + 1)-colourings has diameter Θ(|V | 2 ).

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.

One of the main goals of sensor networks is to provide accurate information about a sensing field for an extended period of time. This requires collecting measurements from as many sensors as possible to have a better view of the sensor surroundings. However, due to energy limitations and to prolong the network lifetime, the number of active sensors should be kept to a minimum. To resolve this conflict of interest, sensor selection schemes are used. In this paper, we survey different schemes that are used to select sensors. Based on the purpose of selection, we classify the schemes into (1) coverage schemes, (2) target tracking and localization schemes, (3) single mission assignment schemes and (4) multiple missions assignment schemes. We also look at solutions to relevant problems from other areas and consider their applicability to sensor networks. Finally, we take a look at the open research problems in this field.

Abstract. We perform a systematic study in the computational complexity of the connected variant of three related transversal problems: Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. Just like their original counterparts, these variants are NP-complete for general graphs. A graph G is H-free for some graph H if G contains no induced subgraph isomorphic to H. It is known that Connected Vertex Cover is NP-complete even for H-free graphs if H contains a claw or a cycle. We show that the two other connected variants also remain NP-complete if H contains a cycle or claw. In the remaining case H is a linear forest. We show that Connected Vertex Cover, Connected Feedback Vertex Set, and Connected Odd Cycle Transversal are polynomial-time solvable for sP2-free graphs for every constant s ≥ 1. For proving these results we use known results on the price of connectivity for vertex cover, feedback vertex set, and odd cycle transversal. This is the first application of the price of connectivity that results in polynomial-time algorithms.