Results 291 to 300 of about 1,321,651 (326)

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.
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Applications of the crossing number

Algorithmica, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pach, J., Shahrokhi, F., Szegedy, M.
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Crossing Number is NP-Complete

SIAM Journal on Algebraic Discrete Methods, 1983
The general crossing number decision problem is defined as follows: ''Given a graph G (multiple edges are allowed) and an integer k, is the crossing number of G less than or equal to k?'' The authors prove that the crossing number decision problem is NP-complete, and hence likely to be intractable.
Garey, M. R., Johnson, D. S.
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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.
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Cross-Number Puzzles

The Arithmetic Teacher, 1980
A cross-number puzzle can be used as a learning device or as a means of evaluation. If it is used as a test, the fact that it is a puzzle may reduce the fear of taking a test. Checking a crossnumber puzzle test is an easy task for the teacher since the answers are in a definite position.
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On stable crossing numbers

Journal of Graph Theory, 1978
AbstractResults giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for G = Qn × K4.4, cry(G)‐m(G) = 4m, for 0 ⩽ = m ⩽ 2n. A generalization is obtained, for certain repeated cartesian products of bipartite graphs. Nonorientable analogs are also developed.
Kainen, Paul C., White, Arthur T.
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The Minor Crossing Number

SIAM Journal on Discrete Mathematics, 2006
The minor crossing number of a graph G is defined as the minimum crossing number of all graphs that contain G as a minor. Basic properties of this new invariant are presented. We study topological structure of graphs with bounded minor crossing number and obtain a new strong version of a lower bound based on the genus.
Drago Bokal, Gasper Fijavz, Bojan Mohar
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Crossing Numbers of Complete Graphs

2017
This chapter examines crossing numbers. When a particular graph is drawn on a given surface, what is the smallest possible number of crossings among the edges? The chapter is organized as follows. Section 1 introduces crossing numbers; reviews the surfaces D, R 2, S, M, P, and T and some connections between them; and gives some basic ...
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Crossing Numbers

2009
R. Bruce Richter, G. Salazar
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Crossing numbers of graphs

1973
Bibliography: p. 157-172.
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