We present a data structure that in a dynamic graph of treedepth at most d, which is modified over time by edge insertions and deletions, maintains an optimumheight elimination forest. The data structure achieves worst-case update time 2 O(d 2 ) , which matches the best known parameter dependency in the running time of a static fpt algorithm for computing the treedepth of a graph. This improves a result of Dvořák et al. [ESA 2014], who for the same problem achieved update time f (d) for some non-elementary (i.e. tower-exponential) function f . As a by-product, we improve known upper bounds on the sizes of minimal obstructions for having treedepth d from doubly-exponential in d to d O(d) .As applications, we design new fully dynamic parameterized data structures for detecting long paths and cycles in general graphs. More precisely, for a fixed parameter k and a dynamic graph G, modified over time

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Uwagi recenzyjne i polemiczne po lekturze pracy Małgorzaty Ewy Stefaniuk Preambuła aktu normatywnego w doktrynie oraz w procesie stanowienia i stosowania polskiego prawa w latach 1989-2007,Warszawa 2009

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In a previously published article (Przegląd Sejmowy No. 5(142)/2017) the authors proposed definitions of the following concepts: normativity, redundancy and uselessness of a legal text. The article provides a typological review of Polish legal texts. The authors analysed the basic units of the integral (articulated) part of normative acts, i.e. legal provisions, showing their normativity, redundancy, and uselessness. The analyse includes: internal preambles, provisions describing the object and subject scope of the act, legal principles, programme and task provisions, meliorative provisions, emendations, permanently unrealisable regulations, legal definitions. The analyses led to identification of four basic types of errors in legal provisions, which were named: “doubles”, “widows”, “orphans”, and “botches”. In their closing remarks, the authors signalled the need to supplement the analysis with a description of non-integral (non-articulated) parts of normative acts. Another part of the study, devoted to these problems, is currently being prepared.