List coloring in the absence of a linear forest.

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H

A Satisfiability-based Approach for Embedding Generalized Tanglegrams on Level Graphs

A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in computational biology to compare evolutionary histories of species. In this paper we present a formulation of two related combinatorial embedding problems concerning tanglegrams in terms of CNF-formulas. The first problem is known as planar embedding and the second as crossing minimization problem. We show that our satisfiability formulation of these problems can handle a much more general case with more than two, not necessarily binary or complete, trees defined on arbitrary sets of leaves and allowed to vary their layouts

Risk of betel chewing for oesophageal cancer in Taiwan

Among 104 cases of squamous-cell oesophageal carcinoma patients and 277 controls in Taiwan, after adjusting for cigarette smoking, alcohol consumption, and other confounders, we found that subjects who chewed from 1 to 495 betel-year and more than 495 betel-years (about 20 betel quid per day for 20 years) had 3.6-fold (95% Cl = 1.3–10.1) and 9.2-fold risk (95% Cl = 1.8–46.7), respectively, of developing oesophageal cancer, compared to those who did not chew betel. © 2001 Cancer Research Campaign http://www.bjcancer.co

Open problems on graph coloring for special graph classes.

For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c:V→{1,2,…}c:V→{1,2,…} such that c(u)≠c(v)c(u)≠c(v) for every edge uv∈Euv∈E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring

Arterial bicarbonate is associated with hypoxic burden and uncontrolled hypertension in obstructive sleep apnea - The ESADA cohort

Objective: Blood bicarbonate concentration plays an important role for obstructive sleep apnea (OSA) patients to maintain acid-base balance. We investigated the association between arterial standard bicarbonate ([HCO3-]) and nocturnal hypoxia as well as comorbid hypertension in OSA. Methods: A cross-sectional analysis of 3329 patients in the European Sleep Apnea Database (ESADA) was performed. Arterial blood gas analysis and lung function test were performed in conjunction with polysomnographic sleep studies. The 4% oxygen desaturation index (ODI), mean and minimum oxygen saturation (SpO2), and percentage of time with SpO2 below 90% (T90%) were used to reflect nocturnal hypoxic burden. Arterial hypertension was defined as a physician diagnosis of hypertension with ongoing antihypertensive medication. Hypertensive patients with SBP/DBP below or above 140/90 mmHg were classified as controlled-, uncontrolled hypertension, respectively. Results: The [HCO3-] level was normal in most patients (average 24.0 ± 2.5 mmol/L). ODI, T90% increased whereas mean and minimum SpO2 decreased across [HCO3-] tertiles (ANOVA, p = 0.030, <0.001, <0.001, and <0.001, respectively). [HCO3-] was independently associated with ODI, mean SpO2, minimum SpO2, and T90% after adjusting for confounders (β value [95%CI]: 1.21 [0.88–1.54], −0.16 [-0.20 to −0.11], −0.51 [-0.64 to −0.37], 1.76 [1.48–2.04], respectively, all p < 0.001). 1 mmol/L elevation of [HCO3-] was associated with a 4% increased odds of uncontrolled hypertension (OR: 1.04 [1.01–1.08], p = 0.013). Conclusion: We first demonstrated an independent association between [HCO3-] and nocturnal hypoxic burden as well as uncontrolled hypertension in OSA patients. Bicarbonate levels as an adjunctive measure provide insight into the pathophysiology of hypertension in OSA