We estimate the chromatic number of graphs whose vertex set is the set of edges of a complete geometric graph on n points, and adjacency is defined in terms of geometric disjointness or geometric intersection.

Motivation Since the identification of the novel coronavirus (SARS-CoV-2), the scientific community has made a huge effort to understand the virus biology and to develop vaccines. Next-generation sequencing strategies have been successful in understanding the evolution of infectious diseases as well as facilitating the development of molecular diagnostics and treatments. Thousands of genomes are being generated weekly to understand the genetic characteristics of this virus. Efficient pipelines are needed to analyze the vast amount of data generated. Here we present a new pipeline designed for genomic analysis and variant identification of the SARS-CoV-2 virus. Results PipeCoV shows better performance when compared to well-established SARS-CoV-2 pipelines, with a lower content of Ns and higher genome coverage when compared to the Wuhan reference. It also provides a variant report not offered by other tested pipelines. Availability https://github.com/alvesrco/pipecov.

The first known families of cages arised from the incidence graphs of generalized polygons of order q, q a prime power. In particular, (q + 1, 6)-cages have been obtained from the projective planes of order q. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on F q .In this paper, we introduce some combinatorial operations to construct new infinite families of small regular graphs of girth 7 from the (q + 1, 8)-cages arising from the generalized quadrangles of order q, q a prime power.

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