Results 41 to 50 of about 9,538,132 (298)
Parameterised Partially-Predrawn Crossing Number [PDF]
, 2022 Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number.
Hliněný, Petr; orcid: +2 more
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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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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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Journal of Graph Algorithms and Applications, 2012 In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if the two edges share no endpoint.
Radoslav Fulek +3 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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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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Software Solution of the Algorithm of the Cyclic-Order Graph [PDF]
Acta Electrotechnica et Informatica, 2018 In this paper we describe by pseudo-code the ``Algorithm of the cyclic-order graph'', which we programmed in MATLAB 2016a and which is also possible to be executed in GNU Octave. We describe program's functionality and its use.
Štefan Berežný +2 more
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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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On the crossing number of join product of the discrete graph with special graphs of order five
Electronic Journal of Graph Theory and Applications, 2020 The main aim of the paper is to give the crossing number of join product G+Dn for the disconnected graph G of order five consisting of the complete graph K4 and of one isolated vertex.
Michal Staš
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Cyclic Permutations in Determining Crossing Numbers
Discussiones Mathematicae Graph Theory, 2022 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.
Klešč Marián, Staš Michal
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