A contribution to the second neighborhood problem

Seymour's Second Neighborhood Conjecture asserts that every digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We prove this conjecture for classes of digraphs whose missing graph is a comb, a complete graph minus 2 independent edges, or a complete graph minus the edges of a cycle of length 5

Surgical care for the direct and indirect victims of violence in the eastern Democratic Republic of Congo

ABSTRACT: BACKGROUND: The provision of surgical assistance in conflict is often associated with care for victims of violence. However, there is an increasing appreciation that surgical care is needed for non-traumatic morbidities. In this paper we report on surgical interventions carried out by Medecins sans Frontieres in Masisi, North Kivu, Democratic Republic of Congo to contribute to the scarce evidence base on surgical needs in conflict. METHODS: We analysed data on all surgical interventions done at Masisi district hospital between September 2007 to December 2009. Types of interventions are described, and logistic regression used to model associations with violence-related injury. RESULTS: 2869 operations were performed on 2441 patients. Obstetric emergencies accounted for over half (675, 57%) of all surgical pathology and infections for another quarter (160, 14%). Trauma-related injuries accounted for only one quarter (681, 24%) of all interventions; among these, 363 (13%) were violence-related. Male gender (adjusted odds ratio (AOR)=20.0, p<0.001), military status (AOR=4.1, p<0.001), and age less than 20 years (AOR=2.1, p<0.001) were associated with violence-related injury. Immediate peri-operative mortality was 0.2%. CONCLUSIONS: In this study, most surgical interventions were unrelated to violent trauma and rather reflected the general surgical needs of a low-income tropical country. Programs in conflict zones in low-income countries need to be prepared to treat both the war-wounded and non-trauma related life-threatening surgical needs of the general population. Given the limited surgical workforce in these areas, training of local staff and task shifting is recommended to support broad availability of essential surgical care. Further studies into the surgical needs of the population are warranted, including population-based surveys to improve program planning and resource allocation and the effectiveness of the humanitarian response

Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.Comment: v4: Minor changes made following helpful comments by the referee

Prognostic significance of cortactin levels in head and neck squamous cell carcinoma: comparison with epidermal growth factor receptor status

Cortactin is an actin-binding Src substrate involved in cell motility and invasion. In this study, we sought to examine the prognostic importance of cortactin protein expression in head and neck squamous cell carcinoma (HNSCC). To do so, cortactin and EGF receptor (EGFR) expression was retrospectively evaluated by immunohistochemistry in a tissue microarray composed of 176 HNSCCs with a mean follow-up time of 5 years. Cortactin immunoreactivity was weak to absent in normal epithelial tissue. Overexpression of the protein in 77 out of 176 tumours (44%) was associated with more advanced tumour-node-metastasis stage and higher histologic grade. Cortactin overexpression was associated with significantly increased local recurrence rates (49 vs 28% for high and low expressing carcinomas, respectively), decreased disease-free survival (17 vs 61%), and decreased the 5-year overall survival of (21 vs 58%), independently of the EGFR status. In multivariate analysis, cortactin expression status remained an independent prognostic factor for local recurrence, disease-free survival, and overall survival. Importantly, we identified a subset of patients with cortactin-overexpressing tumours that displayed low EGFR levels and a survival rate that equalled that of patients with tumoral overexpression of both EGFR and cortactin. These findings identify cortactin as a relevant prognostic marker and may have implications for targeted therapies in patients with HNSCC

A Unified Approach to Distance-Two Colouring of Graphs on Surfaces

In this paper we introduce the notion of $\Sigma$-colouring of a graph $G$: For given subsets $\Sigma(v)$ of neighbours of $v$, for every $v\in V(G)$, this is a proper colouring of the vertices of $G$ such that, in addition, vertices that appear together in some $\Sigma(v)$ receive different colours. This concept generalises the notion of colouring the square of graphs and of cyclic colouring of graphs embedded in a surface. We prove a general result for graphs embeddable in a fixed surface, which implies asymptotic versions of Wegner's and Borodin's Conjecture on the planar version of these two colourings. Using a recent approach of Havet et al., we reduce the problem to edge-colouring of multigraphs, and then use Kahn's result that the list chromatic index is close to the fractional chromatic index. Our results are based on a strong structural lemma for graphs embeddable in a fixed surface, which also implies that the size of a clique in the square of a graph of maximum degree $\Delta$ embeddable in some fixed surface is at most $\frac32\,\Delta$ plus a constant.Comment: 36 page