Problem 58384. Minimum number of crossings in a complete bipartite graph

  • Created by HH
This problem is related to problem 58389.
A complete bipartite graph may be drawn in different ways, such that the number of line crossings differs between drawings.
To date, the question of how to draw the graph so as to minimize the number of crossings remains unsolved.
Nevertheless, an upper bound can be calculated for the number of crossings, based on the number of elements in each of the two sets comprising the graph's vertices.
Given the number of elements in each set, m and n, calculate the upper bound, b, for the minimum number of line crossings in the resulting complete bipartite graph.
Example:
m = 3;
n = 4;
b = 2
Solve

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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Nov 28, 2023

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graph theory

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