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Abstract Aims The coronavirus disease‐2019 (COVID‐19) pandemic has changed the landscape of medical care delivery worldwide. We aimed to assess the influence of COVID‐19 pandemic on hospital admissions and in‐hospital mortality rate in patients with acute heart failure (AHF) in a retrospective, multicentre study. Methods and results From 1 January 2019 to 31 December 2020, a total of 101 433 patients were hospitalized in 24 Cardiology Departments in Poland. The number of patients admitted due to AHF decreased by 23.4% from 9853 in 2019 to 7546 in 2020 (P

Despite constantly updating our knowledge on atrial fibrillation and flutter there are many questions and doubts about the nature and extent of arrhythmic and non-arrhythmic consequences of these arrhythmias. In part 1 of the state-of-the-art paper the diagnostic work-up of patients with the 2 arrhythmias was summarized. The management of patients with atrial fibrillation and flutter requires a multidisciplinary approach in the risk assessment (including stroke) and treatment strategy. Regardless of the type of antiarrhythmic or anticoagulant therapy, benefits must always surpass or at least offset potential adverse effects and drug toxicity. In part 2 of the state-of-the-art paper, current therapeutic strategies have been summarized.

Despite constantly updating our knowledge on atrial fibrillation and flutter, there are still many questions and doubts about the nature and extent of the arrhythmic and non-arrhythmic consequences of these arrhythmias. In part 1 of the state-of-the-art paper the diagnostic work-up of patients with the 2 arrhythmias has been summarized. The management of patients with atrial fibrillation and flutter requires a multidisciplinary approach in the risk assessment (including stroke) and treatment strategy. Regardless of the type of antiarrhythmic or anticoagulant therapy, benefits must always surpass or at least offset potential adverse effects and drug toxicity.

Background: The coronavirus disease-2019 (COVID-19) pandemic is surging across Poland, leading to many direct deaths and underestimated collateral damage. We aimed to compare the influence of the COVID-19 pandemic on hospital admissions and in-hospital mortality in larger vs. smaller cardiology departments (i.e., with ≥2000 vs.

By \(P_m\) we denote a path of order \(m\). A graph \(G\) is said to be \(P_m\)-saturated if \(G\) has no subgraph isomorphic to \(P_m\) and adding any new edge to \(G\) creates a \(P_m\) in \(G\). In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given \(m\) and \(n\) find the minimum size \(sat(n;P_m)\) of \(P_m\)-saturated graph and characterize the graphs of \(Sat(n;P_m)\) - the set of \(P_m\)-saturated graphs of minimum size. They have solved this problem for \(n\geq a_m\) where \(a_m=\begin{cases}3\cdot 2^{k-1}-2 &\quad\text{ if }\quad m=2k,\, k\gt 2\\ 2^{k+1}-2 &\quad\text{ if }\quad m=2k+1,\, k\geq 2\end{cases}\). We define \(b_m=\begin{cases}3\cdot 2^{k-2} &\quad\text{ if }\quad m=2k,\, k\geq 3\\ 3\cdot 2^{k-1}-1 &\quad\text{ if }\quad m=2k+1,\, k\geq 3\end{cases}\) and give \(sat(n;P_m)\) and \(Sat(n;P_m)\) for \(m\geq 6\) and \(b_m\leq n\leq a_m\).

Graphs and Algorithms