Geometric Spanning Cycles in Bichromatic Point Sets

Given a set of points in the plane each colored either red or blue, we find non-self-intersecting geometric spanning cycles of the red points and of the blue points such that each edge of the red spanning cycle is crossed at most three times by the blue spanning cycle and vice-versa

Nursery production without peat : an insight into peat-free nurseries in the UK

Torvmarker täcker ~3% av världens landyta och har sedan senaste istiden fungerat som en viktig kolsänka, som tar upp koldioxid (CO2) ur atmosfären. Ungefär 10% av torvmarkerna på jorden har dränerats, huvudsakligen för skogs- och lantbruk, samt till viss del för torvbruk. Genom utdikning förlorar torvmarker sin funktion som kolsänka, och i stället ger den utdikade arealen upphov till ett utsläpp av 2 miljarder ton CO2 per år, som motsvarar ~5% av det mänsklig orsakade utsläpp av CO2. Eftersom återvätning av torvmarker kan vända denna process, har många länder satt i gång miljöprogram i syfte att skydda och återställer torvmarker. I Storbritannien har den politiska diskussionen kring torv lett till att användningen av odlingstorv ska fasas ut inom hela trädgårdsbranschen fram till 2030. Även om omsättningen av detta mål är frivilligt, finns det ett flertal plantskolor i Storbritannien som redan idag producerar sina containerodlade växter helt utan torv. Inom ramen för detta arbete kontaktades dessa plantskolor med en enkätundersökning i syfte att ta del av deras erfarenheter med torvfria odlingssystem. Främsta målen med detta var att ta reda på vilka odlingssubstrat dessa torvfria plantskolor använder i stället och att identifiera vilka fördelar och utmaningar som uppstår vid torvfri plantskoleproduktion. Det visade sig att kokosfiber, barkmull, träfiber, grönkompost och komposterad ull är de substratkomponenter som används mest i torvfria odlingssubstrat för containerodling i Storbritannien. Anpassningen av odlingssystemen till torvfria odlingssubstrat baserade på dessa komponenter upplevs av majoriteten som hanterbart. Ur resultaten framgick dock därutom att optimeringen av växtnäringsförsörjningen och bevattningsrutinerna kan upplevas som utmanande och således rekommenderas att dessa arbetsmoment bör kontrolleras noggrant. Dessutom upplevs den delvis begränsade tillgängligheten och varierande kvaliteten av torvfria odlingssubstrat som problematisk. Som fördelaktigt upplever odlarna fram för allt att märkningen som en ”torvfri plantskola” är bra för marknadsföringen och kan således utnyttjas för att attrahera både, privat- och företagskunder, som vill handla hållbart producerade växter. Sammanlagt visar resultaten av detta arbete att det är fullt möjligt att producera ett brett sortiment av olika växtslag helt utan torv, såväl i liten som stor skala, och att en torvfri plantskola kan vara en lönsam affärsmodell.Peatlands cover ~3% of the earth´s land surface and have since the last ice age functioned as an important carbon sink, taking up carbon dioxide (CO2) from the atmosphere. About 10% of the global peatlands have been drained, mainly for forestry and agriculture, and to some extent for peat extraction. Drained peatlands not only lose their function as carbon sinks, but instead give rise to an emission of almost 2 billion tonnes of CO2 per year, which corresponds to ~5% of the human-caused CO2 emissions. Because rewetting of peatlands can reverse this process, many countries have launched environmental programs aimed at protecting and restoring peatlands. In the United Kingdom (UK), the political discussion about peat has led to the decision that the use of peat has to be phased out within the entire horticultural industry by 2030. Although the implementation of this goal is voluntary, there are several nurseries in the UK that already produce their container-grown plants completely without peat. As part of this study, these nurseries were contacted with a survey to take part in their experiences with peat-free cultivation systems. The main objectives of this were to investigate which growing media these peat-free nurseries use to replace peat and to identify the benefits and challenges that arise in peat-free nursery production. The results show that coir, composted bark, wood fibre, green compost and composted wool are the substrate components most used in peat-free growing media for container nursery production in the UK. The adaptation of the cultivation systems to peat-free growing media based on these components is perceived by the majority as manageable. However, the results also showed that the optimisation of plant nutrition and irrigation routines can be perceived as challenging and thus it is recommended that these aspects should be controlled carefully. In addition, the partly limited availability and varying quality of peat-free growing media is perceived as problematic. As main advantage the nurseries experience that the label “peat-free” is good for marketing and can thus be used to attract both, private and corporate customers, who want to buy sustainably produced plants. Overall, the results of this study show that it is possible to produce a wide range of different plant species completely without peat, both on small and large scale, and that a peat-free nursery can be a profitable business model

Simple DFS on the Complement of a Graph and on Partially Complemented Digraphs

A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. A partially complemented digraph $\widetilde{G}$ is a digraph obtained from a sequence of vertex complement operations on $G$. Dahlhaus et al. showed that, given an adjacency-list representation of $\widetilde{G}$, depth-first search (DFS) on $G$ can be performed in $O(n + \widetilde{m})$ time, where $n$ is the number of vertices and $\widetilde{m}$ is the number of edges in $\widetilde{G}$. To achieve this bound, their algorithm makes use of a somewhat complicated stack-like data structure to simulate the recursion stack, instead of implementing it directly as a recursive algorithm. We give a recursive $O(n+\widetilde{m})$ algorithm that uses no complicated data-structures

Connectivity, tree-decompositions and unavoidable-minors

The results in this thesis are steps toward bridging the gap between the handful of exact structure theorems known for minor-closed classes of graphs, and the very general, yet wildly qualitative, Graph Minors Structure Theorem. This thesis introduces a refinement of the notion of tree-width. Tree-width is a measure of how “tree-like” a graph is. Essentially, a graph is tree-like if it can be decomposed across a collection of non-crossing vertex-separations into small pieces. In our variant, which we call k-tree-width, we require that the vertex-separations each have order at most k. Tree-width and branch-width are related parameters in a graph, and we introduce a branch-width-like variant for k-tree-width. We find a dual notion, in terms of tangles, for our branch-width parameter, and we prove a generalization of Robertson and Seymour’s Grid Theorem