Results 271 to 280 of about 9,538,132 (298)

On the parity of crossing numbers

Journal of Graph Theory, 1988
AbstractFor an integer n ⩾ 1, a graph G has an n‐constant crossing number if, for any two good drawings ϕ and ϕ′ of G in the plane, μ(ϕ) ≡ μ(ϕ′) (mod n), where μ(ϕ) is the number of crossings in ϕ. We prove that, except for trivial cases, a graph G has n‐constant crossing number if and only if n = 2 and G is either Kp or Kq,r, where p, q, and r are odd.
Dan Archdeacon, R. Bruce Richter
openaire   +3 more sources

Biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method

Random Structures & Algorithms, 2008
AbstractThe biplanar crossing number cr2(G) of a graph G is min{cr(G1) + cr(G2)}, where cr is the planar crossing number. We show that cr2(G) ≤ (3/8)cr(G). Using this result recursively, we bound the thickness by Θ(G) ‐ 2 ≤ Kcr2(G)0.4057 log2n with some constant K.
Éva Czabarka, Ondrej Sýkora, László A. Székely, Imrich Vrto   +3 more
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On the crossing number of complete graphs

Proceedings of the eighteenth annual symposium on Computational geometry, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oswin Aichholzer, Franz Aurenhammer, Hannes Krasser   +2 more
openaire   +2 more sources

THE ADDITIVITY OF CROSSING NUMBERS

Journal of Knot Theory and Its Ramifications, 2004
It has long been conjectured that the crossing numbers of links are additive under the connected sum of links. This is a difficult problem in knot theory and has been open for more than 100 years. In fact, many questions of much weaker conditions are still open.
openaire   +1 more source

On the crossing number ofcm �cn

Journal of Graph Theory, 1998
We 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, 2018
Ribbon \(2\)-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.
openaire   +1 more source

Observational-based study to explore pedestrian crossing behaviors at signalized and unsignalized crosswalks

Accident Analysis and Prevention, 2021
Kayvan Aghabayk, Ahmad Jafari, Nirajan Shiwakoti   +2 more
exaly  

Crossing Numbers

2009
R. Bruce Richter, G. Salazar
openaire   +1 more source

Development of exact and heuristic optimization methods for safety improvement projects at level crossings under conflicting objectives

Reliability Engineering and System Safety, 2022
Eren Ozguven, Maxim A Dulebenets, John O. Sobanjo   +2 more
exaly  

Shaking table tests on fault-crossing tunnels and aseismic effect of grouting

Tunnelling and Underground Space Technology, 2022
Yong Yuan, Mi Zhao, Haitao Yu
exaly