438 research outputs found

    Kempe equivalence of colourings of cubic graphs

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    Given a graph G=(V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kempe changes. A conjecture of Mohar asserts that, for k≥3, all k-colourings of connected k-regular graphs that are not complete are Kempe equivalent. We address the case k=3 by showing that all 3-colourings of a connected cubic graph G are Kempe equivalent unless G is the complete graph K4 or the triangular prism

    Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration

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    We continue research into a well-studied family of problems that ask whether the vertices of a given graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We consider the case where G is the class of k-degenerate graphs. This problem is known to be polynomial-time solvable if k = 0 (recognition of bipartite graphs), but NP-complete if k = 1 (near-bipartite graphs) even for graphs of maximum degree 4. Yang and Yuan [DM, 2006] showed that the k = 1 case is polynomial-time solvable for graphs of maximum degree 3. This also follows from a result of Catlin and Lai [DM, 1995]. We study the general k ≥ 1 case for n-vertex graphs of maximum degree k + 2 We show how to find A and B in O(n) time for k = 1, and in O(n 2 ) time for k ≥ 2. Together, these results provide an algorithmic version of a result of Catlin [JCTB, 1979] and also provide an algorithmic version of a generalization of Brook’s Theorem, proved by Borodin, Kostochka and Toft [DM, 2000] and Matamala [JGT, 2007]. The results also enable us to solve an open problem of Feghali et al. [JGT, 2016]. For a given graph G and positive integer `, the vertex colouring reconfiguration graph of G has as its vertex set the set of `-colourings of G and contains an edge between each pair of colourings that differ on exactly on vertex. We complete the complexity classification of the problem of finding a path in the reconfiguration graph between two given `-colourings of a given graph of maximum degree k

    Syndecan-2 is a novel target of insulin-like growth factor binding protein-3 and is over-expressed in fibrosis

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    Extracellular matrix deposition and tissue scarring characterize the process of fibrosis. Transforming growth factor beta (TGFβ) and Insulin-like growth factor binding protein-3 (IGFBP-3) have been implicated in the pathogenesis of fibrosis in various tissues by inducing mesenchymal cell proliferation and extracellular matrix deposition. We identified Syndecan-2 (SDC2) as a gene induced by TGFβ in an IGFBP-3-dependent manner. TGFβ induction of SDC2 mRNA and protein required IGFBP-3. IGFBP-3 independently induced production of SDC2 in primary fibroblasts. Using an ex-vivo model of human skin in organ culture expressing IGFBP-3, we demonstrate that IGFBP-3 induces SDC2 ex vivo in human tissue. We also identified Mitogen-activated protein kinase-interacting kinase (Mknk2) as a gene induced by IGFBP-3. IGFBP-3 triggered Mknk2 phosphorylation resulting in its activation. Mknk2 independently induced SDC2 in human skin. Since IGFBP-3 is over-expressed in fibrotic tissues, we examined SDC2 levels in skin and lung tissues of patients with systemic sclerosis (SSc) and lung tissues of patients with idiopathic pulmonary fibrosis (IPF). SDC2 levels were increased in fibrotic dermal and lung tissues of patients with SSc and in lung tissues of patients with IPF. This is the first report describing elevated levels of SDC2 in fibrosis. Increased SDC2 expression is due, at least in part, to the activity of two pro-fibrotic factors, TGFβ and IGFBP-3. © 2012 Ruiz et al

    A Reconfigurations Analogue of Brooks’ Theorem

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    Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless G is a complete graph or a cycle with an odd number of vertices, or k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike. We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter, if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2). We complete this structural classification by settling the missing case: if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2). We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is O(n 2) time solvable for k = 3, PSPACE-complete for 4 ≤ k ≤ Δ(G), O(n) time solvable for k = Δ(G) + 1, O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)

    The Membrane-Associated Adaptor Protein DOK5 Is Upregulated in Systemic Sclerosis and Associated with IGFBP-5-Induced Fibrosis

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    Systemic sclerosis (SSc) is characterized by excessive fibrosis of the skin and internal organs due to fibroblast proliferation and excessive production of extracellular matrix (ECM). We have shown that insulin-like growth factor binding protein (IGFBP)-5 plays an important role in the development of fibrosis in vitro, ex vivo, and in vivo. We identified a membrane-associated adaptor protein, downstream of tyrosine kinase/docking protein (DOK)5, as an IGFBP-5-regulated target gene using gene expression profiling of primary fibroblasts expressing IGFBP-5. DOK5 is a tyrosine kinase substrate associated with intracellular signaling. Our objective was to determine the role of DOK5 in the pathogenesis of SSc and specifically in IGFBP-5-induced fibrosis. DOK5 mRNA and protein levels were increased in vitro by endogenous and exogenous IGFBP-5 in primary human fibroblasts. DOK5 upregulation required activation of the mitogen-activated protein kinase (MAPK) signaling cascade. Further, IGFBP-5 triggered nuclear translocation of DOK5. DOK5 protein levels were also increased in vivo in mouse skin and lung by IGFBP-5. To determine the effect of DOK5 on fibrosis, DOK5 was expressed ex vivo in human skin in organ culture. Expression of DOK5 in human skin resulted in a significant increase in dermal thickness. Lastly, levels of DOK5 were compared in primary fibroblasts and lung tissues of patients with SSc and healthy donors. Both DOK5 mRNA and protein levels were significantly increased in fibroblasts and skin tissues of patients with SSc compared with those of healthy controls, as well as in lung tissues of SSc patients. Our findings suggest that IGFBP-5 induces its pro-fibrotic effects, at least in part, via DOK5. Furthermore, IGFBP-5 and DOK5 are both increased in SSc fibroblasts and tissues and may thus be acting in concert to promote fibrosis

    Knowledge, practice and attitudes regarding antibiotics use among Lebanese dentists

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    Objectives: Explore antibiotic use, assess conformity with evidence-practice guidelines, and describe knowledge and attitudinal factors among Lebanese dentists. Methods: National cross-sectional telephonic survey, using a standardized questionnaire addressing demographic, educational and professional data, usual antibiotics prophylactic and curative prescription pattern and influential factors, knowledge concerning antibiotics use in selected patient-populations, and attitude regarding antimicrobial resistance. Analyses used descriptive statistics, and bivariate analysis to observe predictors of higher knowledge. Results: the overall response rate for the study was around 21%. 322 dentists participated. On average, 17.51% of consultations resulted in antibiotic use; previous antibiotic experience mostly influenced prescriptions (81.3%). Referral of pregnant and lactating women and cardiac patients, when antibiotics are needed, was high (26.9%, 28.5% and 79.4%, respectively). Macrolides were the dominant first-line antibiotics in penicillin allergy (47.4%). Penicillins were most common for pregnant and lactating women. Penicillins (95.0%), 2g (63.9%), and 1 hour pre-procedure (34%) were the main components of prophylaxis for cardiac patients. Prophylactic and curative use varied widely; few dentists exhibited guideline-conform prescriptions. Mean knowledge scores of prophylaxis for cardiac and non-cardiac patients, and antibiotics’ side effects were predominantly poor (46.75±14.82, 39.21±33.09 and 20.27±18.77, respectively over 100). Practicing outside Beirut, undergraduate qualification in Lebanon, and post-graduate qualification predicted higher knowledge. 75.9% acknowledged the contribution of dentistry-based prescribing to antibiotic resistance and 94.7% knew at least one cause of resistance. Conclusions: Dentists show positive attitude towards antimicrobial resistance. Yet, they lack uniformity in antibiotic stewardship. Poor knowledge and guideline-incongruent prophylactic and therapeutic prescribing are observed. Development of targeted interventions is needed to promote judicious antibiotic use within Lebanese dentistry

    Recognizing graphs close to bipartite graphs.

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    We continue research into a well-studied family of problems that ask if the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We let G be the class of k-degenerate graphs. The problem is known to be polynomial-time solvable if k=0 (bipartite graphs) and NP-complete if k=1 (near-bipartite graphs) even for graphs of diameter 4, as shown by Yang and Yuan, who also proved polynomial-time solvability for graphs of diameter 2. We show that recognizing near-bipartite graphs of diameter 3 is NP-complete resolving their open problem. To answer another open problem, we consider graphs of maximum degree D on n vertices. We show how to find A and B in O(n) time for k=1 and D=3, and in O(n^2) time for k >= 2 and D >= 4. These results also provide an algorithmic version of a result of Catlin [JCTB, 1979] and enable us to complete the complexity classification of another problem: finding a path in the vertex colouring reconfiguration graph between two given k-colourings of a graph of bounded maximum degree
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