Results 41 to 50 of about 11,183,836 (302)
Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs
Mathematics, 2023 Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory.
Jana Fortes, Michal Staš
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On the crossing numbers of join products of five graphs of order six with the discrete graph [PDF]
Opuscula Mathematica, 2020 The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product \(G^{\ast} + D_n\), where the disconnected graph \(G^{\ast}\) of order six consists of ...
Michal Staš
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On the crossing number of K13 [PDF]
J. Comb. Theory B, 2013 Since the crossing number of K_{12} is now known to be 150, it is well-known that simple counting arguments and Kleitman's parity theorem for the crossing number of K_{2n+1} combine with a specific drawing of K_{13} to show that the crossing number of K_{
Dan McQuillan +2 more
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ON THE CROSSING NUMBER OF THE JOIN OF FIVE VERTEX GRAPH WITH THE DISCRETE GRAPH Dn [PDF]
Acta Electrotechnica et Informatica, 2017 In this paper, we show the values of crossing numbers for join products of graph G on five vertices with the discrete graph Dn and the path Pn on n vertices. The proof is done with the help of software. The software generates all cyclic permutations for
Štefan BEREŽNÝ, Michal STAŠ
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An Evolutionary Formulation of the Crossing Number Problem
Discrete Dynamics in Nature and Society, 2009 A graph drawing algorithm is presented which results in complete graphs having minimum crossings equal to that of Guy's conjecture. It is then generalized and formulated in an evolutionary algorithm (EA) to perform constrained search for the crossing ...
Che Sheng Gan +3 more
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Discrete Mathematics & Theoretical Computer Science, 2005 An edge in a drawing of a graph is called $\textit{even}$ if it intersects every other edge of the graph an even number of times. Pach and Tóth proved that a graph can always be redrawn such that its even edges are not involved in any intersections.
Michael J. Pelsmajer +2 more
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Mathematics, 2020 The crossing number cr ( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main goal of the paper is to state the crossing number of the join product K 2 , 3 + C n for the complete ...
Michal Staš
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Note on the Pair-crossing Number and the Odd-crossing Number [PDF]
Discrete & Computational Geometry, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Shellable Drawings and the Cylindrical Crossing Number of $$K_{n}$$Kn [PDF]
Discrete & Computational Geometry, 2013 The Harary–Hill Conjecture states that the number of crossings in any drawing of the complete graph $$K_n$$Kn in the plane is at least $$Z(n):=\frac{1}{4}\left\lfloor \frac{n}{2}\right\rfloor \left\lfloor \frac{n-1}{2}\right\rfloor \left\lfloor \frac{n-2}
B. Ábrego +4 more
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Crossing number of Cartesian product of prism and path
AKCE International Journal of Graphs and Combinatorics, 2020 An m-prism is the Cartesian product of an m-cycle and a path with 2 vertices. We prove that the crossing number of the join of an m-prism () and a graph with k isolated vertices is km for each We then use this result to prove that the crossing number of ...
Yip C. Yiew, Gek L. Chia, Poh-Hwa Ong
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