Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane $z=0$ and edges are unobstructed lines of sight parallel to the $x$- or $y$-axis. We prove that: $(i)$ Every complete bipartite graph admits a 2.5D-BR; $(ii)$ The complete graph $K_n$ admits a 2.5D-BR if and only if $n \leq 19$; $(iii)$ Every graph with pathwidth at most $7$ admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an $n$-vertex graph that admits a 2.5D-GBR has at most $4n - 6 \sqrt{n}$ edges and this bound is tight. Finally, we prove that deciding whether a given graph $G$ admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR $\Gamma$ is the set of bottom faces of the boxes in $\Gamma$.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Characterization of Clavibacter michiganensis subsp. michiganensis strains from recent outbreaks of bacterial wilt and canker in Serbia

Milijasevic-Marcic S, Gartemann K-H, Frohwitter J, et al. Characterization of Clavibacter michiganensis subsp. michiganensis strains from recent outbreaks of bacterial wilt and canker in Serbia. European Journal Of Plant Pathology. 2012;134(4):697-711.Sixty-eight Clavibacter michiganensis subsp. michiganensis (Cmm) strains from recent outbreaks of bacterial wilt and canker in Serbia were collected from several tomato growing regions during a three-year period. The pathogen was identified based on bacteriological characteristics and pathogenicity tests and the identity of strains was confirmed by DAS ELISA and PCR amplification using primers CMM5/6 and PSA4/R. The strains showed homogeneity in biochemical and physiological properties. However, pathogenicity tests revealed differences in virulence that are presumably due to a loss of the pat-1 gene. Further strain characterization using DNA-based methods revealed a high diversity of the Serbian Cmm strains. Based on multi-locus sequence typing (MLST) analyses of five genes, Cmm strains were divided into seven groups. The pulsed-field gel electrophoresis (PFGE) pattern of a selection of strains supported the groupings based on trees of the kdpA/sdhA sequences. On the other hand, groupings made according to PFGE and MLST were not correlated to plasmid content in all cases. This study suggested that high genetic variability of the Serbian Cmm strains was detected both in MLST and PFGE analyses, and could have resulted either from new Cmm strains being introduced by seeds from different origins or as a consequence of an intraspecific hybridization process. In addition, this study proposed MLST as an efficient tool in epidemiological studies, population biology investigations and tracking the routes of transmission of pathogens. Four of the five house-keeping genes (kdpA, sdhA, ligA and gyrB) selected to characterize Cmm strains proved to be suitable for the MLST analysis. This is the first study carried out on the characterization of Cmm using MLST