Colouring (Pr + Ps)-Free Graphs

The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u)⊆{1,…,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. The graph Pr+Ps is the disjoint union of the r-vertex path Pr and the s-vertex path Ps. We prove that List 3-Colouring is polynomial-time solvable for (P2+P5)-free graphs and for (P3+P4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices

Universal mechanism of discontinuity of commensurate-incommensurate transitions in three-dimensional solids: Strain dependence of soliton self-energy

We show that there exists a universal mechanism of long-range soliton attraction in three-dimensional solids and, therefore, of discontinuity of any commensurate-incommensurate (C-IC) phase transition. This mechanism is due to the strain dependence of the soliton self-energy and specific features of the solid-state elasticity. The role of this mechanism is studied in detail for a class of C-IC transitions where the IC modulation is one-dimensional, the anisotropy in the order parameter space is small, and the symmetry of the systems allows the existence of the Lifshitz invariant. Two other mechanisms of soliton attraction are operative here but the universal mechanism considered in this paper is found to be the most important one in some cases. Comparison with the most extensively studied C-IC transition in $\rm K_2SeO_4$ shows that the experimentally observed thermal anomalies can be understood as a result of the smearing of the theoretically predicted discontinuous transition.Comment: 8 pages (extended version, title changed

Colouring (Pr+Ps)-free graphs.

The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs

Morphological, biochemical and physiological traits of upper and lower canopy leaves of European beech tend to converge with increasing altitude

The present work has explored for the first time acclimation of upper versus lower canopy leaves along an altitudinal gradient. We tested the hypothesis that restrictive climatic conditions associated with high altitudes reduce within-canopy variations of leaf traits. The investigated beech (Fagus sylvatica L.) forest is located on the southern slope of the Hrubý Jeseník Mountains (Czech Republic). All measurements were taken on leaves from upper and lower parts of the canopy of mature trees (>85 years old) growing at low (400 m above sea level, a.s.l.), middle (720 m a.s.l.) and high (1100 m a.s.l.) altitudes. Compared with trees at higher altitudes, those growing at low altitudes had lower stomatal conductance, slightly lower CO2 assimilation rate (Amax) and leaf mass per area (LMA), and higher photochemical reflectance index, water-use efficiency and Rubisco content. Given similar stand densities at all altitudes, the different growth conditions result in a more open canopy and higher penetration of light into lower canopy with increasing altitude. Even though strong vertical gradients in light intensity occurred across the canopy at all altitudes, lower canopy leaves at high altitudes tended to acquire the same morphological, biochemical and physiological traits as did upper leaves. While elevation had no significant effect on nitrogen (N) and carbon (C) contents per unit leaf area, LMA, or total content of chlorophylls and epidermal flavonoids in upper leaves, these increased significantly in lower leaves at higher altitudes. The increases in N content of lower leaves were coupled with similar changes in Amax. Moreover, a high N content coincided with high Rubisco concentrations in lower but not in upper canopy leaves. Our results show that the limiting role of light in lower parts of the canopy is reduced at high altitudes. A great capacity of trees to adjust the entire canopy is thus demonstrated

Fifth European Dirofilaria and Angiostrongylus Days (FiEDAD) 2016

Peer reviewe

Genome of Diuraphis noxia, a global aphid pest of small grains

Background: The Russian wheat aphid, Diuraphis noxia Kurdjumov, is one of the most important pests of small grains throughout the temperate regions of the world. This phytotoxic aphid causes severe systemic damage symptoms in wheat, barley, and other small grains as a direct result of the salivary proteins it injects into the plant while feeding.Results: We sequenced and de novo assembled the genome of D. noxia Biotype 2, the strain most virulent to resistance genes in wheat. The assembled genomic scaffolds span 393 MB, equivalent to 93% of its 421 MB genome, and contains 19,097 genes. D. noxia has the most AT-rich insect genome sequenced to date (70.9%), with a bimodal CpG(O/E) distribution and a complete set of methylation related genes. The D. noxia genome displays a widespread, extensive reduction in the number of genes per ortholog group, including defensive, detoxification, chemosensory, and sugar transporter groups in comparison to the Acyrthosiphon pisum genome, including a 65% reduction in chemoreceptor genes. Thirty of 34 known D. noxia salivary genes were found in this assembly. These genes exhibited less homology with those salivary genes commonly expressed in insect saliva, such as glucose dehydrogenase and trehalase, yet greater conservation among genes that are expressed in D. noxia saliva but not detected in the saliva of other insects. Genes involved in insecticide activity and endosymbiont-derived genes were also found, as well as genes involved in virus transmission, although D. noxia is not a viral vector.Conclusions: This genome is the second sequenced aphid genome, and the first of a phytotoxic insect. D. noxia's reduced gene content of may reflect the influence of phytotoxic feeding in shaping the D. noxia genome, and in turn in broadening its host range. The presence of methylation-related genes, including cytosine methylation, is consistent with other parthenogenetic and polyphenic insects. The D. noxia genome will provide an important contrast to the A. pisum genome and advance functional and comparative genomics of insects and other organisms.Peer reviewedBiochemistry and Molecular Biolog