Prehliadanie podľa Autor "Haviar, Miroslav"
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Položka Characterizations of kites as graceful graphs(Department of mathematics and statistics of the Universidad de La Frontera : Temuco, 2024) Haviar, Miroslav; Kotuľová, KatarínaWe introduce and study an infinite family of graceful graphs, which we call kites. The kites are graphs where a path is joined with a graph "forming" a kite. We study and characterize three classes of the kites: kites formed by cycles known to be graceful, fan kites and lantern kites. Beside showing in a transparent way that all these graphs are graceful, we provide characterizations of these graphs among all simple graphs via three tools: via Sheppard's labelling sequences introduced in the 1970s and via labelling relations and graph chessboards. The latter are relatively new tools for the study of graceful graphs introduced by Haviar and Iva\v ska in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a~nice visualization of the graceful labellings.Položka Dual digraphs of finite meet-distributive and modular lattices(Department of mathematics and statistics of the Universidad de La Frontera : Temuco, 2024) Craig Andrew, P. K.; Haviar, Miroslav; Marais, KlariseWe describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015). These digraphs, known as TiRS digraphs, have their origins in the dual representations of lattices by Urquhart (1978) and Ploščica (1995). We describe two properties of finite lattices which are weakenings of (upper) semimodularity and lower semimodularity respectively, and then show how these properties have a simple description in the dual digraphs. Combined with previous work in this journal on dual digraphs of semidistributive lattices (2022), it leads to a dual representation of finite meet-distributive lattices. This provides a natural link to finite convex geometries. In addition, we present two sufficient conditions on a finite TiRS digraph for its dual lattice to be modular. We close by posing three open problems.Položka Factor principal congruences and Boolean products in filtral varieties(Springer Nature Switzerland AG : Basel, 2024) Davey, Brian A.; Haviar, MiroslavMotivated by Haviar and Ploščica’s 2021 characterisation of Boolean products of simple De Morgan algebras, we investigate Boolean products of simple algebras in filtral varieties. We provide two main theorems. The first yields Werner’s Boolean-product representation of algebras in a discriminator variety as an immediate application. The second, which applies to algebras in which the top congruence is compact, yields a generalisation of the Haviar–Ploščica result to semisimple varieties of Ockham algebras. The property of having factor principal congruences is fundamental to both theorems. While major parts of our general theorems can be derived from results in the literature, we offer new, self-contained and essentially elementary proofs.Položka Fostering critical thinking in higher education through a coaching approach: theory and practical applications(Belianum. Vydavateľstvo Univerzity Mateja Bela v Banskej Bystrici, 2020) Theodoulides, Lenka; Niklová, Miriam; Liptáková, Katarína; Nafoussi, Gabriela; Haviar, MiroslavPoložka Rozvoj kritického myslenia koučovacím prístupom vo vysokoškolskom prostredí(Belianum. Vydavateľstvo Univerzity Mateja Bela v Banskej Bystrici, 2020) Theodoulides, Lenka; Haviar, Miroslav; Šošková, Ivana; Niklová, Miriam; Liptáková, Katarína; Biloveský, Vladimír; Nafoussi (Kormancová), Gabriela; Kubišová, Ľuboslava