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

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

A Characterization of Graphs with Small Palette Index

Given an edge-coloring of a graph G, we associate to every vertex v of G the set of colors appearing on the edges incident with v. The palette index of G is defined as the minimum number of such distinct sets, taken over all possible edge-colorings of G. A graph with a small palette index admits an edge-coloring which can be locally considered to be almost symmetric, since few different sets of colors appear around its vertices. Graphs with palette index 1 are r-regular graphs admitting an r-edge-coloring, while regular graphs with palette index 2 do not exist. Here, we characterize all graphs with palette index either 2 or 3 in terms of the existence of suitable decompositions in regular subgraphs. As a corollary, we obtain a complete characterization of regular graphs with palette index 3

An explicit formula for obtaining (q+1,8)(q+1,8)-cages and others small regular graphs of girth 8

Let $q$ be a prime power; $(q+1,8)$-cages have been constructed as incidence graphs of a non-degenerate quadric surface in projective 4-space $P(4, q)$. The first contribution of this paper is a construction of these graphs in an alternative way by means of an explicit formula using graphical terminology. Furthermore by removing some specific perfect dominating sets from a $(q+1,8)$-cage we derive $k$-regular graphs of girth 8 for $k= q-1$ and $k=q$, having the smallest number of vertices known so far

Families of Small Regular Graphs of Girth 5

In this paper we obtain $(q+3)$--regular graphs of girth 5 with fewer vertices than previously known ones for $q=13,17,19$ and for any prime $q \ge 23$ performing operations of reductions and amalgams on the Levi graph $B_q$ of an elliptic semiplane of type ${\cal C}$. We also obtain a 13-regular graph of girth 5 on 236 vertices from $B_{11}$ using the same technique

Heterogeneity and penetration of HIV-1 non-subtype B viruses in an Italian province: Public health implications

SUMMARYThis study assessed changes in prevalence and distribution of HIV-1 non-subtype B viruses in Italian and immigrant patients over two decades in a province in Italy. All HIV-positive patients who underwent genotypic resistance testing were selected. Prevalence of non-subtype B viruses in 3-year periods was calculated. All sequences of non-subtype B and those provided by REGA as unassigned were analysed for phylogenetic relationships. In total, 250/1563 (16%) individuals were infected with a non-subtype B virus. Prevalence increased over time, reaching a peak (31·5%) in 2004–2006. In Italian patients, the most frequent subtypes were B (92·5%) and F1 (4%). F1 subtype was also prevalent in patients from South America (13·6%); in patients of African origin, CRF02_AG (54·9%) and G (12·3%) were the most frequent. HIV-1 non-subtype B infections in Italians were mostly found in patients who acquired HIV sexually. A phylogenetic relationship between F subtypes in Italian and representative HIV-1 sequences from Brazil was found. C subtypes in Italians were phylogenetically related to subtypes circulating in Brazil. Inter-subtype recombinants were also found in the latest years. The HIV-1 epidemic in Brescia province evolved to the point where about 1/3 patients recently diagnosed harboured non-B HIV subtypes. The distribution of HIV-1 non-B subtypes in Italian patients resembled that in South American patients and phylogenetic relatedness between some Italian and South American HIV-1 strains was found. The possible epidemiological link between these two populations would have been missed by looking only at risk factors for HIV acquisition declared by patients. The evidence of inter-subtype recombinants points to significant genetic assortment. Overall our results support phylogenetic analysis as a tool for epidemiological investigation in order to guide targeted prevention strategies

Adaptation to an amoeba host drives selection of virulence-associated traits in Vibrio cholerae.

Predation by heterotrophic protists drives the emergence of adaptive traits in bacteria, and often these traits lead to altered interactions with hosts and persistence in the environment. Here we studied adaptation of the cholera pathogen, Vibrio cholerae during long-term co-incubation with the protist host, Acanthamoeba castellanii. We determined phenotypic and genotypic changes associated with long-term intra-amoebal host adaptation and how this impacts pathogen survival and fitness. We showed that adaptation to the amoeba host leads to temporal changes in multiple phenotypic traits in V. cholerae that facilitate increased survival and competitive fitness in amoeba. Genome sequencing and mutational analysis revealed that these altered lifestyles were linked to non-synonymous mutations in conserved regions of the flagellar transcriptional regulator, flrA. Additionally, the mutations resulted in enhanced colonisation in zebrafish, establishing a link between adaptation of V. cholerae to amoeba predation and enhanced environmental persistence. Our results show that pressure imposed by amoeba on V. cholerae selects for flrA mutations that serves as a key driver for adaptation. Importantly, this study provides evidence that adaptive traits that evolve in pathogens in response to environmental predatory pressure impact the colonisation of eukaryotic organisms by these pathogens

Foreign Policy and the Ideology of Post-ideology: The Case of Matteo Renzi’s Partito Democratico

The post-communist Italian Left has experienced a long phase of ideational misalignment between ideas placed at different levels, as a qualified discursive institutionalist approach demonstrates. Background public philosophies have often clashed with post-communist political ideology, while foreign policy programmes have often contradicted specific policies. Under the leadership of Matteo Renzi, however, the PD is now experiencing a moment of remarkable ideational consistency. Rather than being founded on entirely new premises, this new consensus folds old elements into new ones and shows all the defining traits of post-ideology. Yet, by espousing post-ideology, Renzi is making an ultimately ideological move whose limitations may soon start to show