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On the crossing number ofcm �cn
Journal of Graph Theory, 1998We show that the M-crossing number crM(Cm × Cn) of Cm × Cn behaves asymptotically according to limn∞ {crM(Cm × Cn)/((m − 2)n)} = 1, for each m ≥ 3. This result reinforces the conjecture cr(Cm × Cn) = (m − 2)n if 3 ≤ m ≤ n, which has been proved only for m ≤ 6. © 1998 John Wiley & Sons, Inc. J.
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Ribbon crossing numbers, crossing numbers, and Alexander polynomials
Topology and its Applications, 2018Ribbon \(2\)-knotted objects are locally flat embeddings of surfaces in \(4\)-space which bound immersed \(3\)-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. Let \(K^2\) be a ribbon \(2\)-knot.
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From Local Pair-Crossing Number to Local Crossing Number.
We prove that if a graph can be drawn in the plane such that each edge crosses at most k other edges, then it can be redrawn so that each edge participates in at most k³+O(k²) crossings. This improves the previous exponential bound that follows from a result of Schaefer and Štefankovič and answers a question of Ackerman and Schaefer.Fox, Jacob, Pach, János, Suk, Andrew
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Shaking table tests on fault-crossing tunnels and aseismic effect of grouting
Tunnelling and Underground Space Technology, 2022Yong Yuan, Mi Zhao, Haitao Yu
exaly
Effects of above-crossing tunnelling on the existing shield tunnels
Tunnelling and Underground Space Technology, 2016Rongzhu Liang, Yi Hong, Tangdai Xia
exaly