Preprinti (MII) / Preprints

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Browsing Preprinti (MII) / Preprints by Author "Zeps, Dainis"

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    How to draw combinatorial maps?
    (2013-01-31) Zeps, Dainis; Ķikusts, Paulis
    In this article we consider the combinatorial map (rendered by permutations) approach to graphs on surfaces and how between both could be establish some terminological uniformity in favor of combinatorial maps in the way rotations were set as fundamental structural elements, and other necessary notions were derived from them. We call this the rotational prevalence with respect to how to build a graph drawing environment. We deal here with simple operations of how to draw combinatorial maps and partial maps. One of our aims would be to advocate a wider use of combinatorial maps in the graph drawing applications. Besides, we advocate to use corners of halfedges where upon permutations act in place of halfedges.
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    On building 4-critical plane and projective plane multiwheels from odd wheels
    (2013-01-31) Zeps, Dainis
    We build unbounded classes of plane and projective plane multiwheels that are 4-critical that are received summing odd wheels as edge sums modulo two. These classes can be considered as ascending from a single common graph that can be received as an edge sum modulo two of the octahedron graph O and the minimal wheel W_3. All graphs of these classes belong to 2n-2-edges-class of graphs, among which are those that quadrangulate projective plane, i.e., graphs from the Grötzsch class received applying Mycielski's Construction to an odd cycle.
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    ON CYCLE INVARIANT
    (2013-04-23) Zeps, Dainis
    Taking the programming paradigm with the cycle invariant as a base notion there for a ground cycle paradigm, in a more general setting here these things are considered. Epistemological aspects with reference to Rene Descartes methods of reasoning are considered. Particularly analogy between Descartes method of specification and top-down programming is considered. A general principle of reconstruction in epistemology is suggested and discussed, firstly specifying it within programming and then trying it to generalize to whatever else. Submitted as a paper in philosophy for doctoral studies.
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    On Grinbergs' differential geometry and finite fields
    (2019-03-27) Zeps, Dainis
    Emanuels Grinbergs, in his youth, during ten years, from 1933 until 1943, wrote three dissertations on one subject, namely, differential geometry [1, 2, 3]. We think that his work in this direction has been neglected for many years, and it is the last time to try to understand the significance of these works. Here, in this short article we touch only one aspect of this work, and compare and put together two approaches, one from thesis of Grinbergs [3], and another, of the author's, [5, 6], where we show close relation between both.
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    Testing 4-critical plane and projective plane multiwheels using Mathematica
    (2015-10-27) Zeps, Dainis
    In this article we explore 4-critical graphs using Mathematica. We generate graph patterns according [1, D. Zeps. On building 4-critical plane and projective plane multiwheels from odd wheels, arXiv:1202.4862v1]. Using the base graph, minimal planar multiwheel and in the same time minimal according projective pattern built multiwheel, we build minimal multiwheels according [1], Weforward two conjectures according graphs augmented according considered patterns and their 4-criticallity, and argue them to be proved here if the paradigmatic examples of this article are accepted to be parts of proofs.
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    Using 2-colorings in the theory of uniquely Hamiltonian graphs
    (2019-02) Zeps, Dainis;
    We use the concept of 2-coloring in analyzing UH3 graphs and building exact specifications of functions to find new UH3 graphs by Hamiltonian cycle edge extractions