Generation of cubic graphs and snarks with large girth

We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least $k\ge 5$ which are very efficient for $5\le k \le 7$ and show how these algorithms can be efficiently restricted to generate snarks with girth at least $k$. Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with girth at least 6 and 7, respectively. Using these generators we have also generated all non-isomorphic snarks with girth at least 6 up to 38 vertices and show that there are no snarks with girth at least 7 up to 42 vertices. We present and analyse the new list of snarks with girth 6.Comment: 27 pages (including appendix

Ramsey numbers R(K3,G) for graphs of order 10

In this article we give the generalized triangle Ramsey numbers R(K3,G) of 12 005 158 of the 12 005 168 graphs of order 10. There are 10 graphs remaining for which we could not determine the Ramsey number. Most likely these graphs need approaches focusing on each individual graph in order to determine their triangle Ramsey number. The results were obtained by combining new computational and theoretical results. We also describe an optimized algorithm for the generation of all maximal triangle-free graphs and triangle Ramsey graphs. All Ramsey numbers up to 30 were computed by our implementation of this algorithm. We also prove some theoretical results that are applied to determine several triangle Ramsey numbers larger than 30. As not only the number of graphs is increasing very fast, but also the difficulty to determine Ramsey numbers, we consider it very likely that the table of all triangle Ramsey numbers for graphs of order 10 is the last complete table that can possibly be determined for a very long time.Comment: 24 pages, submitted for publication; added some comment

Generation of cubic graphs

We describe a new algorithm for the efficient generation of all non-isomorphic connected cubic graphs. Our implementation of this algorithm is more than 4 times faster than previous generators. The generation can also be efficiently restricted to cubic graphs with girth at least 4 or 5

House of Graphs: a database of interesting graphs

In this note we present House of Graphs (http://hog.grinvin.org) which is a new database of graphs. The key principle is to have a searchable database and offer -- next to complete lists of some graph classes -- also a list of special graphs that already turned out to be interesting and relevant in the study of graph theoretic problems or as counterexamples to conjectures. This list can be extended by users of the database.Comment: 8 pages; added a figur

Results of the CoreOrganic-Workshop on animal based parameters in Trenthorst, Germany (04.02.08-08.02.2008)

It was the aim of this meeting to train the assessors of several CoreOrganic-Partners (i.e. Austria, Germany, Denmark and Norway) with regard to the methods which are going to be applied in the course of the project on-farm assessments. Training involved animal-based parameters, a resource checklist and a management questionnaire. After a theoretical and practical introduction, inter-observer reliability (IOR) of the main animal-based parameters was tested. This included gait scoring/lameness, body condition, cleanliness and integument alterations. The scoring systems for gait scoring, cleanliness and integument alterations had been adapted from the WelfareQuality® protocol; body condition was scored according to Metzner et al. (1993). Subjective scoring systems which are used in many epidemiological studies have the advantage that they do not require any equipment but - due to the subjectivity of the assessment - it is necessary to achieve acceptable inter-observer reliability (IOR) before and after the study to ensure valid data

The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

Interdisziplinär betrachtet: Gesundheit- und Leistungsfähigkeit von Milchkühen im Ökologischen Landbau

Mastitis, metabolic disorders and lameness are still the most important diseases in German organic dairy herds and cause enormous financial losses as well as pain in the animals suffering from these diseases. This project focuses on the development of prevention-oriented health management strategies in organic dairy farms and aims to validate this approach through an interdisciplinary on-farm intervention study. In total 14 institutions are involved. To assess the risk of metabolic disorders and mastitis a national field survey of 100 organic dairy farms is used considering the system of production from the plant populations of the grassland, the quality of feedstuff to housing conditions and milk quality to name but a few examples of the data recorded during farm visits. The study relies on a small team of scientists and consultants and is complemented by investigations carried out on experimental stations. These experiments deal with the improvement of grassland, feed intake, and the relation between metabolic disorders and udder infections

Ramsey numbers R(K3, G) for graphs of order 10

In this article we give the generalized triangle Ramsey numbers R(K3,G) of 12 005 158 of the 12 005 168 graphs of order 10. There are 10 graphs remaining for which we could not determine the Ramsey number. Most likely these graphs need approaches focusing on each individual graph in order to determine their triangle Ramsey number. The results were obtained by combining new computational and theoretical results. We also describe an optimized algorithm for the generation of all maximal triangle-free graphs and triangle Ramsey graphs. All Ramsey numbers up to 30 were computed by our implementation of this algorithm. We also prove some theoretical results that are applied to determine several triangle Ramsey numbers larger than 30. As not only the number of graphs is increasing very fast, but also the difficulty to determine Ramsey numbers, we consider it very likely that the table of all triangle Ramsey numbers for graphs of order 10 is the last complete table that can possibly be determined for a very long time

Dairy health in German organic farming - an intervention study on lameness and the implementation of herd health plans

A pilot study carried out in 2002/2003 (50 farms) revealed that production diseases such as mastitis, lameness and metabolic disorders play a considerable role in german organic dairy farming. In a follow-up project, an intervention study on lameness is currrently being carried out in 43 cubicle housed Holstein Friesian herds. Farms are monitored at 3-months intervals for two years. The average baseline lameness prevalence was 26%. Preliminary findings suggest a beneficial effect of access to pasture during summer and improvements due to intervention measures (housing, management) taken in approximately half of the farms. In a third step, herd health plans with regard to mastitis, lameness, metabolic disorders, reproductive disorders and calf diseases will be implemented on the project farms integrating farmers, veterinary practitioners and advisors