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In his PhD thesis [Structural aspects of switching classes, Leiden Institute of Advanced Computer Science, 2001] Hage posed the following problem: “characterize the maximum size graphs in switching classes”. These are called s-maximal graphs. In this paper, we study the properties of such graphs. In particular, we show that any graph with sufficiently large minimum degree is s-maximal, we prove that join of two s-maximal graphs is also an s-maximal graph, we give complete characterization of triangle-free...
The main focus of combinatorial dynamics is put on the structure of periodic points (and the corresponding orbits) of topological dynamical systems. The first result in this area is the famous Sharkovsky's theorem which completely describes the coexistence of periods of periodic points for a continuous map from the closed unit interval to itself. One feature of this theorem is that it can be proved using digraphs of a special type (the so-called periodic graphs). In this paper we use Markov graphs...
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