The number of 2-edge-colored complete graphs with unique hamiltonian alternating cycle

Let G be a 2-edge-colored complete graph of even order n. A cycle of G is alternating if any two successive edges differ in color. We prove that there is a one-to-one correspondence between the set of bipartite tournaments of order n admitting a unique hamiltonian cycle and the set of 2-edge-colored complete graphs of order n admitting a unique alternating hamiltonian cycle. © 2002 Elsevier Science B.V. All rights reserve

Hamiltonian problems in edge-colored complete graphs and eulerian cycles in edge-colored graphs : some complexity results

ou

Rationale and Design of the Efficacy of a Standardized Diuretic Protocol in Acute Heart Failure Study

Aims: Although acute heart failure (AHF) with volume overload is treated with loop diuretics, their dosing and type of administration are mainly based upon expert opinion. A recent position paper from the Heart Failure Association (HFA) proposed a step-wise pharmacologic diuretic strategy to increase the diuretic response and to achieve rapid decongestion. However, no study has evaluated this protocol prospectively. Methods and results: The Efficacy of a Standardized Diuretic Protocol in Acute Heart Failure (ENACT-HF) study is an international, multicentre, non-randomized, open-label, pragmatic study in AHF patients on chronic loop diuretic therapy, admitted to the hospital for intravenous loop diuretic therapy, aiming to enrol 500 patients. Inclusion criteria are as follows: at least one sign of volume overload (oedema, ascites, or pleural effusion), use ≥ 40 mg of furosemide or equivalent for >1 month, and a BNP > 250 ng/L or an N-terminal pro-B-type natriuretic peptide > 1000 pg/L. The study is designed in two sequential phases. During Phase 1, all centres will treat consecutive patients according to the local standard of care. In the Phase 2 of the study, all centres will implement a standardized diuretic protocol in the next cohort of consecutive patients. The protocol is based upon the recently published HFA algorithm on diuretic use and starts with intravenous administration of two times the oral home dose. It includes early assessment of diuretic response with a spot urinary sodium measurement after 2 h and urine output after 6 h. Diuretics will be tailored further based upon these measurements. The study is powered for its primary endpoint of natriuresis after 1 day and will be able to detect a 15% difference with 80% power. Secondary endpoints are natriuresis and diuresis after 2 days, change in congestion score, change in weight, in-hospital mortality, and length of hospitalization. Conclusions: The ENACT-HF study will investigate whether a step-wise diuretic approach, based upon early assessment of urinary sodium and urine output as proposed by the HFA, is feasible and able to improve decongestion in AHF with volume overload

Heart failure in Europe: Guideline-directed medical therapy use and decision making in chronic and acute, pre-existing and de novo, heart failure with reduced, mildly reduced, and preserved ejection fraction – the ESC EORP Heart Failure III Registry

Aims We analysed baseline characteristics and guideline-directed medical therapy (GDMT) use and decisions in theEuropean Society of Cardiology (ESC) Heart Failure (HF) III Registry. Methods and results Between1November 2018and31December 2020,10162 patients with acute HF (AHF, 39%, age 70 [62-79],36% women) or outpatient visit for HF (61%, age 66 [58-75], 33% women), with HF with reduced (HFrEF, 57%),mildly reduced (HFmrEF,17%) or preserved (HFpEF, 26%) ejection fraction were enrolled from 220 centres in 41European or ESC-affiliated countries. With AHF, 97% were hospitalized, 2.2% received intravenous treatment in theemergency department, and 0.9% received intravenous treatment in an outpatient clinic. AHF was seen by most bya general cardiologist (51%) and outpatient HF most by a HF specialist (48%). A majority had been hospitalized forHF before, but 26% of AHF and 6.1% of outpatient HF had de novo HF. Baseline use, initiation and discontinuation ofGDMT varied according to AHF versus outpatient HF, de novo versus pre-existing HF, and by ejection fraction. Afterthe AHF event or outpatient HF visit, use of any renin-angiotensin system inhibitor, angiotensin receptor-neprilysininhibitor, beta-blocker, mineralocorticoid receptor antagonist and loop diuretics was 89%, 29%, 92%, 78%, and 85%in HFrEF; 89%, 9.7%, 90%, 64%, and 81% in HFmrEF; and 77%, 3.1%, 80%, 48%, and 80% in HFpEF. ConclusionUse and initiation of GDMT was high in cardiology centres in Europe, compared to previous reports from cohortsand registries including more primary care and general medicine and regions more local or outside of Europe andESC-affiliated countries....................................