Results 21 to 30 of about 1,321,651 (326)
On the crossing numbers of join products of W_{4}+P_{n} and W_{4}+C_{n} [PDF]
Opuscula Mathematica, 2021 The crossing number \(\mathrm{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings over all drawings of \(G\) in the plane. The main aim of the paper is to give the crossing number of the join product \(W_4+P_n\) and \(W_4+C_n\) for the ...
Michal Staš, Juraj Valiska
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Odd Crossing Number and Crossing Number Are Not the Same [PDF]
Discrete & Computational Geometry, 2006 The crossing number \(\text{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings, taken over all drawing of \(G\) in the plane. Similarly \(\text{per}(G)\) (respectively \(\text{ocr}(G)\)) denotes the minimum number of pairs of edges which cross at least once (respectively an odd number of times), over all drawings of \(G\) in the plane ...
Pelsmajer, Michael J. +2 more
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The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
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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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The crossing numbers of join products of four graphs of order five with paths and cycles [PDF]
Opuscula Mathematica, 2023 The crossing number \(\mathrm{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings over all drawings of \(G\) in the plane. In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths ...
Michal Staš, Mária Timková
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Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 We define a variant of the crossing number for an embedding of a graphGinto ℝ3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the rectilinear space crossing numbers of pseudo-random graphs.
Bukh, Boris, Hubard, Alfredo
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ALTERNATIVE PROOF ON THE CROSSING NUMBER OF K1,1,3,N [PDF]
Acta Electrotechnica et Informatica, 2019 The main aim of the paper is to give the crossing number of join product G+Dn for the connected graph G of order five isomorphic with the complete tripartite graph K1,1,3, where Dn consists on n isolated vertices.
Michal STAS
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On the pseudolinear crossing number [PDF]
, 2014 A drawing of a graph is {\em pseudolinear} if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The {\em pseudolinear crossing number} of a graph $G$ is the minimum number of pairwise crossings of edges
Hernandez-Velez, Cesar +2 more
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Crossing number, pair-crossing number, and expansion
Journal of Combinatorial Theory, Series B, 2004 The crossing number \(\text{cr}(G)\) of a graph \(G\) is the minimum possible number of edge crossings in a drawing of \(G\) in the plane, and the pair-crossing number \( \text{pcr}(G)\) of a graph \(G\) is smallest number of pairs of crossing edges in any drawing of \(G\) in the plane.
Kolman, Petr, Matoušek, Jiřı́
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