Browsing by Subject "fault-tolerance"

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Access status: Open Access ,
Minimum k-critical-bipartite graphs: the irregular case
(Wydawnictwa AGH, 2026) Cichacz-Przeniosło, Sylwia; Görlich, Agnieszka; Suchan, Karol
We study the problem of finding a minimum \(k\)-critical-bipartite graph of order \((n,m)\): a bipartite graph \(G=(U,V;E)\), with \(|U|=n\), \(|V|=m\), and \(n\gt m\gt 1\), which is \(k\)-critical-bipartite, and the tuple \((|E|, \Delta_U, \Delta_V)\), where \(\Delta_U\) and \(\Delta_V\) denote the maximum degree in \(U\) and \(V\), respectively, is lexicographically minimum over all such graphs. \(G\) is \(k\)-critical-bipartite if deleting any set of at most \(k=n-m\) vertices from \(U\) yields \(G'\) that has a complete matching, i.e., a matching of size \(m\). Cichacz and Suchan solved the problem for biregular bipartite graphs. Here, we extend their results to bipartite graphs that are not biregular. We prove tight lower bounds on the connectivity of \(k\)-critical-bipartite graphs, and we show that \(k\)-critical-bipartite graphs are expander graphs.
Access status: Open Access ,
Techniki programistyczne stosowane w niezawodnych komputerowych systemach sterowania
(Wydawnictwa AGH, 2009) Szymczyk, Magdalena; Szymczyk, Piotr
Computer systems have existed for over 50 years and surround us so much. They are invisible but problem of their reliability is now very actual. Computers hardware, software becomes so complicated that possibility of its improper operation is much bigger. This article presents available software technologies for more reliable computer control systems with their analysis and comparison.