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52690 results in Statistics and Probability

Page 326 of 2635

  • Improved Ramsey-type results for comparability graphs

  • Part of
  • Dániel Korándi, István Tomon
  • Journal:
    Combinatorics, Probability and Computing / Volume 29 / Issue 5 / September 2020
    Published online by Cambridge University Press:
    13 August 2020, pp. 747-756

  • Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is the union of r comparability (or more generally, perfect) graphs, then either G or its complement contains a clique of size $n^{1/(r+1)}$.

    This bound is known to be tight for $r=1$. The question whether it is optimal for $r\ge 2$ was studied by Dumitrescu and Tóth. We prove that it is essentially best possible for $r=2$, as well: we introduce a probabilistic construction of two comparability graphs on n vertices, whose union contains no clique or independent set of size $n^{1/3+o(1)}$.

    Using similar ideas, we can also construct a graph G that is the union of r comparability graphs, and neither G nor its complement contain a complete bipartite graph with parts of size $cn/{(log n)^r}$. With this, we improve a result of Fox and Pach.

  • PES volume 34 issue 3 Cover and Back matter

  • Journal:
    Probability in the Engineering and Informational Sciences / Volume 34 / Issue 3 / July 2020
    Published online by Cambridge University Press:
    12 August 2020, pp. b1-b2
    • Article
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  • Capsular polysaccharide and lipopolysaccharide O type analysis of Klebsiella pneumoniae isolates by genotype in China

  • Z. Y. Zhang, R. Qin, Y. H. Lu, J. Shen, S. Y. Zhang, C. Y. Wang, Y. Q. Yang, F. P. Hu, P. He
  • Journal:
    Epidemiology & Infection / Volume 148 / 2020
    Published online by Cambridge University Press:
    12 August 2020, e191
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  • Klebsiella pneumoniae is a common pathogen associated with nosocomial infections and is characterised serologically by capsular polysaccharide (K) and lipopolysaccharide O antigens. We surveyed a total of 348 non-duplicate K. pneumoniae clinical isolates collected over a 1-year period in a tertiary care hospital, and determined their O and K serotypes by sequencing of the wbb Y and wzi gene loci, respectively. Isolates were also screened for antimicrobial resistance and hypervirulent phenotypes; 94 (27.0%) were identified as carbapenem-resistant (CRKP) and 110 (31.6%) as hypervirulent (hvKP). isolates fell into 58 K, and six O types, with 92.0% and 94.2% typeability, respectively. The predominant K types were K14K64 (16.38%), K1 (14.66%), K2 (8.05%) and K57 (5.46%), while O1 (46%), O2a (27.9%) and O3 (11.8%) were the most common. CRKP and hvKP strains had different serotype distributions with O2a:K14K64 (41.0%) being the most frequent among CRKP, and O1:K1 (26.4%) and O1:K2 (17.3%) among hvKP strains. Serotyping by gene sequencing proved to be a useful tool to inform the clinical epidemiology of K. pneumoniae infections and provides valuable data relevant to vaccine design.

Page 326 of 2635