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    Wyświetlanie 1-9 z 9
    Tytuł:
    Some crossing numbers of products of cycles
    Autorzy:
    Klešč, Marián
    Powiązania:
    https://bibliotekanauki.pl/articles/744339.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    cycle
    Cartesian product
    Opis:
    The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 197-210
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The crossing numbers of certain Cartesian products
    Autorzy:
    Klešč, Marián
    Powiązania:
    https://bibliotekanauki.pl/articles/971930.pdf
    Data publikacji:
    1995
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    path
    Cartesian product
    Opis:
    In this article we determine the crossing numbers of the Cartesian products of given three graphs on five vertices with paths.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1995, 15, 1; 5-10
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the crossing numbers of G □ Cₙ for graphs G on six vertices
    Autorzy:
    Draženská, Emília
    Klešč, Marián
    Powiązania:
    https://bibliotekanauki.pl/articles/743871.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    cycle
    drawing
    crossing number
    Cartesian product
    Opis:
    The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. The crossing numbers of G☐Cₙ for some graphs G on five and six vertices and the cycle Cₙ are also given. In this paper, we extend these results by determining crossing numbers of Cartesian products G☐Cₙ for some connected graphs G of order six with six and seven edges. In addition, we collect known results concerning crossing numbers of G☐Cₙ for graphs G on six vertices.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 239-252
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The crossing numbers of join products of paths with graphs of order four
    Autorzy:
    Klešč, Marián
    Schrötter, Stefan
    Powiązania:
    https://bibliotekanauki.pl/articles/743896.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    path
    crossing number
    join product
    Opis:
    Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing numbers for join of paths with all graphs of order four, as well as for join of all graphs of order four with n isolated vertices are given.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 321-331
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cyclic Permutations in Determining Crossing Numbers
    Autorzy:
    Klešč, Marián
    Staš, Michal
    Powiązania:
    https://bibliotekanauki.pl/articles/32222545.pdf
    Data publikacji:
    2022-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    join product
    cyclic permutation
    Opis:
    The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied. In the paper, we extend know results concerning crossing numbers of join products of small graphs with discrete graphs. The crossing number of the join product G*+ Dn for the disconnected graph G* consisting of five vertices and of three edges incident with the same vertex is given. Up to now, the crossing numbers of G + Dn were done only for connected graphs G. In the paper also the crossing numbers of G*+ Pn and G* + Cn are given. The paper concludes by giving the crossing numbers of the graphs H + Dn, H + Pn, and H + Cn for four different graphs H with |E(H)| ≤ |V (H)|. The methods used in the paper are new. They are based on combinatorial properties of cyclic permutations.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1163-1183
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The crossing numbers of products of a 5-vertex graph with paths and cycles
    Autorzy:
    Klešč, Marián
    Powiązania:
    https://bibliotekanauki.pl/articles/744243.pdf
    Data publikacji:
    1999
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    path
    cycle
    Cartesian product
    Opis:
    There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with "small" graphs. Let H be the 5-vertex graph defined from K₅ by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H × Pₙ and H × Cₙ, showing that in the general case the corresponding crossing numbers are 3n-1, and 3n for even n or 3n+1 if n is odd.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1999, 19, 1; 59-69
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Crossing Numbers of Products of Path with Graphs of Order Six
    Autorzy:
    Klešč, Marián
    Petrillová, Jana
    Powiązania:
    https://bibliotekanauki.pl/articles/30146431.pdf
    Data publikacji:
    2013-07-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    Cartesian product
    path
    tree
    Opis:
    The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path $ P_n $ of length $ n $, the crossing numbers of Cartesian products $ G \square P_n $ for all connected graphs $G$ on five vertices are also known. In this paper, the crossing numbers of Cartesian products $ G \square P_n $ for graphs $ G $ of order six are studied. Let $ H $ denote the unique tree of order six with two vertices of degree three. The main contribution is that the crossing number of the Cartesian product $ H \square P_n $ is $ 2(n − 1) $. In addition, the crossing numbers of $ G \square P_n $ for fourty graphs $G$ on six vertices are collected.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 3; 571-582
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Crossing Numbers of Cartesian Products of Wheels and Trees
    Autorzy:
    Klešč, Marián
    Petrillová, Jana
    Valo, Matúš
    Powiązania:
    https://bibliotekanauki.pl/articles/31341838.pdf
    Data publikacji:
    2017-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    join product
    Cartesian product
    Opis:
    Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given. Afterwards, using Bokal’s zip product operation, the crossing numbers of the Cartesian products of the wheel Wn and all trees T with maximum degree at most five are established.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 2; 399-413
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
    Autorzy:
    Klešč, Marián
    Schrötter, Štefan
    Powiązania:
    https://bibliotekanauki.pl/articles/30146429.pdf
    Data publikacji:
    2013-07-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    Cartesian product
    join product
    star
    Opis:
    The crossing number $ \text{cr}(G) $ of a graph $ G $ is the minimal number of crossings over all drawings of $ G $ in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of crossing numbers were obtained. The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. Moreover, except of six graphs, the crossing numbers of Cartesian products $ G \square K_{1,n} $ for all other connected graphs $ G $ on five vertices are known. In this paper we are dealing with the Cartesian products of stars with graphs on six vertices. We give the exact values of crossing numbers for some of these graphs and we summarise all known results concerning crossing numbers of these graphs. Moreover, we give the crossing number of $ G_1 \square T $ for the special graph $ G_1 $ on six vertices and for any tree $ T $ with no vertex of degree two as well as the crossing number of $ K_{1,n} \square T $ for any tree $ T $ with maximum degree five.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 3; 583-597
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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