Even Orientations and Pfaffian graphs

We give a characterization of Pfaffian graphs in terms of even orientations, extending the characterization of near bipartite non--pfaffian graphs by Fischer and Little \cite{FL}. Our graph theoretical characterization is equivalent to the one proved by Little in \cite{L73} (cf. \cite{LR}) using linear algebra arguments

A formulation of a (q+1,8)-cage

Let $q\ge 2$ be a prime power. In this note we present a formulation for obtaining the known $(q+1,8)$-cages which has allowed us to construct small $(k,g)$--graphs for $k=q-1, q$ and $g=7,8$. Furthermore, we also obtain smaller $(q,8)$-graphs for even prime power $q$.Comment: 14 pages, 2 figure

Even Orientations of Graphs: Part I

A graph G is 1-extendable if every edge belongs to at least one 1-factor. Let G be a graph with a 1-factor F. Then an even F-orientation of G is an orientation in which each F-alternating cycle has exactly an even number of edges directed in the same fixed direction around the cycle. In this paper, we examine the structure of 1-extendible graphs G which have no even F-orientation where F is a fixed 1-factor of G. In the case of cubic graphs we give a characterization. In a companion paper [M. Abreu, D. Labbate and J. Sheehan. Even orientations of graphs: Part II], we complete this characterization in the case of regular graphs, graphs of connectivity at least four and k--regular graphs for $k\ge3$. Moreover, we will point out a relationship between our results on even orientations and Pfaffian graphs developed in [M. Abreu, D. Labbate and J. Sheehan. Even orientations and Pfaffian graphs].Comment: 40 pages, 2 figure

A note on 2--bisections of claw--free cubic graphs

A \emph{$k$--bisection} of a bridgeless cubic graph $G$ is a $2$--colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes have order at most $k$. Ban and Linial conjectured that {\em every bridgeless cubic graph admits a $2$--bisection except for the Petersen graph}. In this note, we prove Ban--Linial's conjecture for claw--free cubic graphs

A construction of small (q-1)-regular graphs of girth 8

In this note we construct a new infinite family of $(q-1)$-regular graphs of girth $8$ and order $2q(q-1)^2$ for all prime powers $q\ge 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself.Comment: 8 pages, 2 figure

The function of integron-associated gene cassettes in Vibrio species: The tip of the iceberg

The integron is a genetic element that incorporates mobile genes termed gene cassettes into a reserved genetic site via site-specific recombination. It is best known for its role in antibiotic resistance with one type of integron, the class 1 integron, a major player in the dissemination of antibiotic resistance genes across Gram negative pathogens and commensals. However, integrons are ancient structures with over 100 classes (including class 1) present in bacteria from the broader environment. While, the class 1 integron is only one example of an integron being mobilized into the clinical environment, it is by far the most successful. Unlike clinical class 1 integrons which are largely found on plasmids, other integron classes are found on the chromosomes of bacteria and carry diverse gene cassettes indicating a non-antibiotic resistance role(s). However, there is very limited knowledge on what these alternative roles are. This is particularly relevant to Vibrio species where gene cassettes make up approximately 1-3% of their entire genome. In this review, we discuss how emphasis on class 1 integron research has resulted in a limited understanding by the wider research community on the role of integrons in the broader environment. This has the capacity to be counterproductive in solving or improving the antibiotic resistance problem into the future. Furthermore, there is still a significant lack of knowledge on how gene cassettes in Vibrio species drive adaptation and evolution. From research in Vibrio rotiferianus DAT722, new insight into how gene cassettes affect cellular physiology offers new alternative roles for the gene cassette resource. At least a subset of gene cassettes are involved in host surface polysaccharide modification suggesting that gene cassettes may be important in processes such as bacteriophage resistance, adhesion/biofilm formation, protection from grazers and bacterial aggregation. © 2013 Rapa and Labbate

Deletion of Integron-Associated Gene Cassettes Impact on the Surface Properties of Vibrio rotiferianus DAT722

Background: The integron is a genetic recombination system that catalyses the acquisition of genes on mobilisable elements called gene cassettes. In Vibrio species, multiple acquired gene cassettes form a cassette array that can comprise 1-3% of the bacterial genome. Since 75% of these gene cassettes contain genes encoding proteins of uncharacterised function, how the integron has driven adaptation and evolution in Vibrio species remains largely unknown. A feature of cassette arrays is the presence of large indels. Using Vibrio rotiferianus DAT722 as a model organism, the aim of this study was to determine how large cassette deletions affect vibrio physiology with a view to improving understanding into how cassette arrays influence bacterial host adaptation and evolution. Methodology/Principal Findings: Biological assays and proteomic techniques were utilised to determine how artificially engineered deletions in the cassette array of V. rotiferianus DAT722 affected cell physiology. Multiple phenotypes were identified including changes to growth and expression of outer membrane porins/proteins and metabolic proteins. Furthermore, the deletions altered cell surface polysaccharide with Proton Nuclear Magnetic Resonance on whole cell polysaccharide identifying changes in the carbohydrate ring proton region indicating that gene cassette products may decorate host cell polysaccharide via the addition or removal of functional groups. Conclusions/Significance: From this study, it was concluded that deletion of gene cassettes had a subtle effect on bacterial metabolism but altered host surface polysaccharide. Deletion (and most likely rearrangement and acquisition) of gene cassettes may provide the bacterium with a mechanism to alter its surface properties, thus impacting on phenotypes such as biofilm formation. Biofilm formation was shown to be altered in one of the deletion mutants used in this study. Reworking surface properties may provide an advantage to the bacterium's interactions with organisms such as bacteriophage, protozoan grazers or crustaceans. © 2013 Rapa et al