Results 31 to 40 of about 308,302 (304)
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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The crossing number of the generalized Petersen graph $P[3k,k]$ [PDF]
, 2003 summary:Guy and Harary (1967) have shown that, for $k\ge 3$, the graph $P[2k,k]$ is homeomorphic to the Möbius ladder ${M_{2k}}$, so that its crossing number is one; it is well known that $P[2k,2]$ is planar. Exoo, Harary and Kabell (1981) have shown hat
Fiorini, Stanley, Gauci, John Baptist
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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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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.
Boris Bukh, Alfredo Hubard
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Improvement on the Crossing Number of Crossing-Critical Graphs [PDF]
Discrete & Computational Geometry, 2020 AbstractThe crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. A graph G is k-crossing-critical if its crossing number is at least k, but if we remove any edge of G, its crossing number drops below k.
János Barát, Géza Tóth 0001
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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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Expected Crossing Numbers [PDF]
Electronic Notes in Discrete Mathematics, 2011 The expected value for the weighted crossing number of a randomly weighted graph is studied. A variation of the Crossing Lemma for expectations is proved. We focus on the case where the edge-weights are independent random variables that are uniformly distributed on [0,1].
Bojan Mohar, Tamon Stephen
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Influence of virtual reality training on the roadside crossing judgements of child pedestrians [PDF]
, 2005 The roadside crossing judgments of children aged 7, 9, and 11 years were assessed relative to controls before and after training with a computer-simulated traffic environment.
Morrison, S. +5 more
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