Clique-Stable Set separation in perfect graphs with no balanced skew-partitions

Inspired by a question of Yannakakis on the Vertex Packing polytope of perfect graphs, we study the Clique-Stable Set Separation in a non-hereditary subclass of perfect graphs. A cut (B,W) of G (a bipartition of V(G)) separates a clique K and a stable set S if $K\subseteq B$ and $S\subseteq W$. A Clique-Stable Set Separator is a family of cuts such that for every clique K, and for every stable set S disjoint from K, there exists a cut in the family that separates K and S. Given a class of graphs, the question is to know whether every graph of the class admits a Clique-Stable Set Separator containing only polynomially many cuts. It is open for the class of all graphs, and also for perfect graphs, which was Yannakakis' original question. Here we investigate on perfect graphs with no balanced skew-partition; the balanced skew-partition was introduced in the proof of the Strong Perfect Graph Theorem. Recently, Chudnovsky, Trotignon, Trunck and Vuskovic proved that forbidding this unfriendly decomposition permits to recursively decompose Berge graphs using 2-join and complement 2-join until reaching a basic graph, and they found an efficient combinatorial algorithm to color those graphs. We apply their decomposition result to prove that perfect graphs with no balanced skew-partition admit a quadratic-size Clique-Stable Set Separator, by taking advantage of the good behavior of 2-join with respect to this property. We then generalize this result and prove that the Strong Erdos-Hajnal property holds in this class, which means that every such graph has a linear-size biclique or complement biclique. This property does not hold for all perfect graphs (Fox 2006), and moreover when the Strong Erdos-Hajnal property holds in a hereditary class of graphs, then both the Erdos-Hajnal property and the polynomial Clique-Stable Set Separation hold.Comment: arXiv admin note: text overlap with arXiv:1308.644

Multigraphs without large bonds are wqo by contraction

We show that the class of multigraphs with at most $p$ connected components and bonds of size at most $k$ is well-quasi-ordered by edge contraction for all positive integers $p,k$. (A bond is a minimal non-empty edge cut.) We also characterize canonical antichains for this relation and show that they are fundamental

Induced minors and well-quasi-ordering

A graph $H$ is an induced minor of a graph $G$ if it can be obtained from an induced subgraph of $G$ by contracting edges. Otherwise, $G$ is said to be $H$-induced minor-free. Robin Thomas showed that $K_4$-induced minor-free graphs are well-quasi-ordered by induced minors [Graphs without $K_4$ and well-quasi-ordering, Journal of Combinatorial Theory, Series B, 38(3):240 -- 247, 1985]. We provide a dichotomy theorem for $H$-induced minor-free graphs and show that the class of $H$-induced minor-free graphs is well-quasi-ordered by the induced minor relation if and only if $H$ is an induced minor of the gem (the path on 4 vertices plus a dominating vertex) or of the graph obtained by adding a vertex of degree 2 to the complete graph on 4 vertices. To this end we proved two decomposition theorems which are of independent interest. Similar dichotomy results were previously given for subgraphs by Guoli Ding in [Subgraphs and well-quasi-ordering, Journal of Graph Theory, 16(5):489--502, 1992] and for induced subgraphs by Peter Damaschke in [Induced subgraphs and well-quasi-ordering, Journal of Graph Theory, 14(4):427--435, 1990]

Induced minors and well-quasi-ordering

International audienceA graph H is an induced minor of a graph G if it can be obtained from an induced subgraph of G by contracting edges. Otherwise, G is said to be H-induced minor-free. Robin Thomas showed in [Graphs without K 4 and well-quasi-ordering, Journal of Combinatorial Theory, Series B, 38(3):240 – 247, 1985] that K 4-induced minor-free graphs are well-quasi ordered by induced minors. We provide a dichotomy theorem for H-induced minor-free graphs and show that the class of H-induced minor-free graphs is well-quasi-ordered by the induced minor relation if and only if H is an induced minor of the gem (the path on 4 vertices plus a dominating vertex) or of the graph obtained by adding a vertex of degree 2 to the complete graph on 4 vertices.Similar dichotomy results were previously given by Guoli Ding in [Subgraphs and well-quasi-ordering, Journal of Graph Theory, 16(5):489–502, 1992] for subgraphs and Peter Damaschke in [Induced subgraphs and well-quasi-ordering, Journal of Graph Theory, 14(4):427–435, 1990] for induced subgraphs

Molecular Basis of Rare Aminoglycoside Susceptibility and Pathogenesis of Burkholderia pseudomallei Clinical Isolates from Thailand

Burkholderia pseudomallei is the etiologic agent of melioidosis, an emerging tropical disease. Because of low infectious dose, broad-host-range infectivity, intrinsic antibiotic resistance and historic precedent as a bioweapon, B. pseudomallei was listed in the United States as a Select Agent and Priority Pathogen of biodefense concern by the US Centers for Disease Control and Prevention and the National Institute of Allergy and Infectious Diseases. The mechanisms governing antibiotic resistance and/or susceptibility and virulence in this bacterium are not well understood. Most clinical and environmental B. pseudomallei isolates are highly resistant to aminoglycosides, but susceptible variants do exist. The results of our studies with three such variants from Thailand reveal that lack of expression or deletion of an efflux pump is responsible for this susceptibility. The large deletion present in one strain not only removes an efflux pump but also several putative virulence genes, including an entire siderophore gene cluster. Despite this deletion, the strain is fully virulent in an acute mouse melioidosis model. In summary, our findings shed light on mechanisms of antibiotic resistance and pathogenesis. They also validate the previously advocated use of laboratory-constructed, aminoglycoside susceptible efflux pump mutants in genetic manipulation experiments

Polar Lipids of Burkholderia pseudomallei Induce Different Host Immune Responses

Melioidosis is a disease in tropical and subtropical regions of the world that is caused by Burkholderia pseudomallei. In endemic regions the disease occurs primarily in humans and goats. In the present study, we used the goat as a model to dissect the polar lipids of B. pseudomallei to identify lipid molecules that could be used for adjuvants/vaccines or as diagnostic tools. We showed that the lipidome of B. pseudomallei and its fractions contain several polar lipids with the capacity to elicit different immune responses in goats, namely rhamnolipids and ornithine lipids which induced IFN-γ, whereas phospholipids and an undefined polar lipid induced strong IL-10 secretion in CD4(+) T cells. Autologous T cells co-cultured with caprine dendritic cells (cDCs) and polar lipids of B. pseudomallei proliferated and up-regulated the expression of CD25 (IL-2 receptor) molecules. Furthermore, we demonstrated that polar lipids were able to up-regulate CD1w2 antigen expression in cDCs derived from peripheral blood monocytes. Interestingly, the same polar lipids had only little effect on the expression of MHC class II DR antigens in the same caprine dendritic cells. Finally, antibody blocking of the CD1w2 molecules on cDCs resulted in decreased expression for IFN-γ by CD4(+) T cells. Altogether, these results showed that polar lipids of B. pseudomallei are recognized by the caprine immune system and that their recognition is primarily mediated by the CD1 antigen cluster

Involvement of the Efflux Pumps in Chloramphenicol Selected Strains of Burkholderia thailandensis: Proteomic and Mechanistic Evidence

Burkholderia is a bacterial genus comprising several pathogenic species, including two species highly pathogenic for humans, B. pseudomallei and B. mallei. B. thailandensis is a weakly pathogenic species closely related to both B. pseudomallei and B. mallei. It is used as a study model. These bacteria are able to exhibit multiple resistance mechanisms towards various families of antibiotics. By sequentially plating B. thailandensis wild type strains on chloramphenicol we obtained several resistant variants. This chloramphenicol-induced resistance was associated with resistance against structurally unrelated antibiotics including quinolones and tetracyclines. We functionally and proteomically demonstrate that this multidrug resistance phenotype, identified in chloramphenicol-resistant variants, is associated with the overexpression of two different efflux pumps. These efflux pumps are able to expel antibiotics from several families, including chloramphenicol, quinolones, tetracyclines, trimethoprim and some β-lactams, and present a partial susceptibility to efflux pump inhibitors. It is thus possible that Burkholderia species can develop such adaptive resistance mechanisms in response to antibiotic pressure resulting in emergence of multidrug resistant strains. Antibiotics known to easily induce overexpression of these efflux pumps should be used with discernment in the treatment of Burkholderia infections

Tame Berge trigraphes

L'objectif de cette thèse est de réussir à utiliser des décompositions de graphes afin de résoudre des problèmes algorithmiques sur les graphes. Notre objet d'étude principal est la classe des graphes de Berge apprivoisés. Les graphes de Berge sont les graphes ne possédant ni cycle de longueur impaire supérieur à 4 ni complémentaire de cycle de longueur impaire supérieure à 4. Dans les années 60, Claude Berge a conjecturé que les graphes de Berge étaient des graphes parfaits. C'est-à-dire que la taille de la plus grande clique est exactement le nombre minimum de couleurs nécessaire à une coloration propre et ce pour tout sous-graphe. En 2002, Chudnovsky, Robertson, Seymour et Thomas ont démontré cette conjecture en utilisant un théorème de structure: les graphes de Berge sont basiques ou admettent une décomposition. Ce résultat est très utile pour faire des preuves par induction. Cependant, une des décompositions du théorème, la skew-partition équilibrée, est très difficile à utiliser algorithmiquement. Nous nous focalisons donc sur les graphes de Berge apprivoisés, c'est-à-dire les graphes de Berge sans skew-partition équilibrée. Pour pouvoir faire des inductions, nous devons adapter le théorème destructure de Chudnovsky et al à notre classe. Nous prouvons un résultat plus fort: les graphes de Berge apprivoisés sont basiques ou admettent une décomposition telle qu'un côté de la décomposition soit toujours basique. Nous avons de plus un algorithme calculant cette décomposition. Nous utilisons ensuite notre théorème pour montrer que les graphes de Berge apprivoisés admettent la propriété du grand biparti, de la clique-stable séparation et qu'il existe un algorithme polynomial permettant de calculer le stable maximum.The goal of this these is to use graph's decompositions to solve algorithmic problems on graphs. We will study the class of Berge tame graphs. A Berge graph is a graph without cycle of odd length at least 4 nor complement of cycle of odd length at least 4.In the 60's, Claude Berge conjectured that Berge graphs are perfect graphs. The size of the biggest clique is exactly the number of colors required to color the graph. In 2002, Chudnovsky, Robertson, Seymour et Thomas proved this conjecture using a theorem of decomposition: Berge graphs are either basic or have a decomposition. This is a useful result to do proof by induction. Unfortunately, one of the decomposition, the skew-partition, is really hard to use. We arefocusing here on Berge tame graphs, i.e~Berge graph without balanced skew-partition. To be able to do induction, we must first adapt the Chudnovsky et al's theorem of structure to our class. We prove a stronger result: Berge tame graphs are basic or have a decomposition such that one side is always basic. We also have an algorithm to compute this decomposition. We then use our theorem to prouve that Berge tame graphs have the big-bipartite property, the clique-stable set separation property and there exists a polytime algorithm to compute the maximum stable set