Results 21 to 30 of about 1,286,422 (323)
Effect of a crossing change on crossing number
, 2011 11 pages, 12 ...
Longting Wu +3 more
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Cubicity, degeneracy, and crossing number
European Journal of Combinatorics, 2013 21 ...
Abhijin Adiga +2 more
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Counting Hamiltonian Cycles in 2-Tiled Graphs
Mathematics, 2021 In 1930, Kuratowski showed that K3,3 and K5 are the only two minor-minimal nonplanar graphs. Robertson and Seymour extended finiteness of the set of forbidden minors for any surface.
Alen Vegi Kalamar +2 more
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The crossing number of the generalized Petersen graph P(3k,k) in the projective plane
AKCE International Journal of Graphs and Combinatorics, 2023 The crossing number of a graph G in a surface Σ, denoted by [Formula: see text], is the minimum number of pairwise intersections of edges in a drawing of G in Σ. Let k be an integer satisfying [Formula: see text], the generalized Petersen graph [Formula:
Jing Wang, Zuozheng Zhang
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The crossing numbers of join products of paths with three graphs of order five [PDF]
Opuscula Mathematica, 2022 The main aim of this paper is to give the crossing number of the join product \(G^\ast+P_n\) for the disconnected graph \(G^\ast\) of order five consisting of the complete graph \(K_4\) and one isolated vertex, where \(P_n\) is the path on \(n\) vertices.
Michal Staš, Mária Švecová
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The crossing numbers of join products of eight graphs of order six with paths and cycles
Karpatsʹkì Matematičnì Publìkacìï, 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. The main aim of this paper is to give the crossing numbers of the join products of eight graphs on six vertices with paths ...
M. Staš
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On the Decay of Crossing Numbers [PDF]
Journal of Combinatorial Theory, Series B, 2007 The crossing number cr(G) of a graph G is the minimum number of crossings over all drawings of G in the plane. In 1993, Richter and Thomassen [RT93] conjectured that there is a constant c such that every graph G with crossing number k has an edge e such that cr(G- e) ≥ k - c√k.
Jacob Fox, Csaba D. Tóth
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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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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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Crossing lemma for the odd-crossing number
Computational Geometry, 2023 A graph is $1$-planar, if it can be drawn in the plane such that there is at most one crossing on every edge. It is known, that $1$-planar graphs have at most $4n-8$ edges. We prove the following odd-even generalization. If a graph can be drawn in the plane such that every edge is crossed by at most one other edge {\em an odd number of times}, then it ...
Karl, János, Tóth, Géza
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