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Applications of the crossing number
Algorithmica, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pach, J., Shahrokhi, F., Szegedy, M.
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THE ADDITIVITY OF CROSSING NUMBERS
Journal of Knot Theory and Its Ramifications, 2004It 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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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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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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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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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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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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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
2017This 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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An ILP-based Proof System for the Crossing Number Problem
Embedded Systems and Applications, 2016Markus Chimani, Tilo Wiedera
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On the crossing number of the join of the discrete graph with one graph of order five
, 2017M. Staš
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On the Crossing Number of Kn without Computer Assistance
Journal of Graph Theory, 2016Dan McQuillan, R. Bruce Richter
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