Thick Forests

We consider classes of graphs, which we call thick graphs, that have their vertices replaced by cliques and their edges replaced by bipartite graphs. In particular, we consider the case of thick forests, which are a subclass of perfect graphs. We show that this class can be recognised in polynomial time, and examine the complexity of counting independent sets and colourings for graphs in the class. We consider some extensions of our results to thick graphs beyond thick forests.Comment: 40 pages, 19 figure

Independent Sets in Asteroidal Triple-Free Graphs

An asteroidal triple (AT) is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called AT-free if it does not have an AT. We show that there is an O(n4 ) time algorithm to compute the maximum weight of an independent set for AT-free graphs. Furthermore, we obtain O(n4 ) time algorithms to solve the INDEPENDENT DOMINATING SET and the INDEPENDENT PERFECT DOMINATING SET problems on AT-free graphs. We also show how to adapt these algorithms such that they solve the corresponding problem for graphs with bounded asteroidal number in polynomial time. Finally, we observe that the problems CLIQUE and PARTITION INTO CLIQUES remain NP-complete when restricted to AT-free graphs

On treewidth approximations

We introduce a natural heuristic for approximating the treewidth of graphs. We prove that this heuristic gives a constant factor approximation for the treewidth of graphs with bounded asteroidal number. Using a different technique, we give a $O(\log k)$ approximation algorithm for the treewidth of arbitrary graphs, where $k$ is the treewidth of the input graph

Independent sets in asteroidal triple-free graphs

An asteroidal triple is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called AT-free if it does not have an asteroidal triple. We show that there is an O(n 2 · (¯m+1)) time algorithm to compute the maximum cardinality of an independent set for AT-free graphs, where n is the number of vertices and ¯m is the number of non edges of the input graph. Furthermore we obtain O(n 2 · (¯m+1)) time algorithms to solve the INDEPENDENT DOMINATING SET and the INDEPENDENT PERFECT DOMINATING SET problem on AT-free graphs. We also show how to adapt these algorithms such that they solve the corresponding problem for graphs with bounded asteroidal number in polynomial time. Finally we observe that the problems CLIQUE and PARTITION INTO CLIQUES remain NP-complete when restricted to AT-free graphs

On the switch Markov chain for perfect matchings

We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. We ask: for which hereditary classes of graphs is the Markov chain ergodic and for which is it rapidly mixing? We provide a precise answer to the ergodicity question and close bounds on the mixing question. We show for the first time that the mixing time of the switch chain is polynomial in the case of monotone graphs, a class that includes examples of interest in the statistical setting

Evaluating the Accuracy of Imputation Methods in a Five-Way Admixed Population

Genotype imputation is a powerful tool for increasing statistical power in an association analysis. Meta-analysis of multiple study datasets also requires a substantial overlap of SNPs for a successful association analysis, which can be achieved by imputation. Quality of imputed datasets is largely dependent on the software used, as well as the reference populations chosen. The accuracy of imputation of available reference populations has not been tested for the five-way admixed South African Colored (SAC) population. In this study, imputation results obtained using three freely-accessible methods were evaluated for accuracy and quality. We show that the African Genome Resource is the best reference panel for imputation of missing genotypes in samples from the SAC population, implemented via the freely accessible Sanger Imputation Server

Prospective Epidemiological Observations on the Course of the Disease in Fibromyalgia Patients

OBJECTIVES: The aim of the study was to carry out a survey in patients with fibromyalgia (FM), to examine their general health status and work incapacity (disability-pension status), and their views on the effectiveness of therapy received, over a two-year observation period. METHODS: 48 patients diagnosed with FM, according to the American College of Rheumatology (ACR) criteria, took part in the study. At baseline, and on average two years later, the patients underwent clinical investigation (dolorimetry, laboratory diagnostics, medical history taking) and completed the Fibromyalgia questionnaire (Dettmer and Chrostek [1]). RESULTS: 27/48 (56%) patients participated in the two-year follow-up. In general, the patients showed no improvement in their symptoms over the observation period, regardless of the type of therapy they had received. General satisfaction with quality of life improved, as did satisfaction regarding health status and the family situation, although the degree of pain experienced remain unchanged. In comparison with the initial examination, there was no change in either work-capacity or disability-pension status. CONCLUSIONS: The FM patients showed no improvement in pain, despite the many various treatments received over the two-year period. The increase in general satisfaction over the observation period was believed to be the result of patient instruction and education about the disease. To what extent a population of patients with FM would show similar outcomes if they did not receive any instruction/education about their disorder, cannot be ascertained from the present study; and, indeed, the undertaking of a study to investigate this would be ethically questionable. As present, no conclusions can be made regarding the influence of therapy on the primary and secondary costs associated with FM

Partitioning a graph into disjoint cliques and a triangle-free graph

A graph G=(V,E) is partitionable if there exists a partition {A,B} of V such that A induces a disjoint union of cliques (i.e., G[A] is P_3-free) and B induces a triangle-free graph (i.e., G[B] is K_3-free). In this paper we investigate the computational complexity of deciding whether a graph is partitionable. The problem is known to be NP-complete on arbitrary graphs. Here it is proved that if a graph G is bull-free, planar, perfect, K_4-free or does not contain certain holes then deciding whether G is partitionable is NP-complete. This answers an open question posed by Thomassé, Trotignon and Vušković. In contrast a finite list of forbidden induced subgraphs is given for partitionable cographs

Surface adhesins and exopolymers of selected foodborne pathogens

The ability of bacteria to bind different compounds and to adhere to biotic and abiotic surfaces provides them with a range of advantages, such as colonization of various tissues, internalisation, avoidance of an immune response and survival and persistence in the environment. A variety of bacterial surface structures are involved in this process and these promote bacterial adhesion in a more or less specific manner. In this review, we will focus on those surface adhesins and exopolymers in selected foodborne pathogens that are involved mainly in primary adhesion. Their role in biofilm development will also be considered when appropriate. Both the clinical impact and implications for food safety of such adhesion will be discussed.The authors are members of the EU COST Action FA1202 (CGAFA1202): A European Network for Mitigating Bacterial Colonisation and Persistence on Foods and Food Processing Environments (http://www.bacfoodnet.org/) and acknowledge this action for facilitating collaborative networking that assisted with this study. The work was further supported by the Ministry of Education, Youth and Sports of the Czech Republic (project COST LD 14015 and project LO1218 under the NPU I program), the 'Cooperation Scientifique Universitaire (CSU)' France Denmark 2012 from the Embassy of France in Denmark 'Institut Francais du Danemark' (IFD) (no. 14/2012/CSU.8.2.1), the EGIDE Programme Hubert Curien (PHC) France Germany PROCOPE 2013 2015 from the 'Ministere des Affaires Etrangeres et Europeennes' (no. 28297WG) and by the Norwegian Research Council (grant no. 192402)