User Tools

    To create and edit articles, please register and log-in

Main Menu : categories & index etc.

Main menu
Click categories to expand

A-Z listingplugin-autotooltip__plain plugin-autotooltip_bigA-Z listing

This is an alphabetical index of all content pages.

Other categories



Also see

Importance Ratings
Curator's rationale
AI Policy

Twitter feed 𝕏

Feeds + s.e.o. etc.
rss / xml feed
sitemap file
A-Z listing (archived)

Indexed under : Mathematics

Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

Turán's brick factory problem

Turán's brick factory problem was devised in 1944 by Hungarian mathematician Pál Turán.

As a WW2 prisoner, Turán had been forced to work in a Transylvanian brick factory, where his job was to move bricks, using hand-pushed rail-carts, from various kilns to various storage yards. All the kilns were connected by rail with all the storage yards. The tracks inevitably (and inconveniently) crossed, leading Turán to wonder “What is the minimum number of crossings?”

Turán's colleague, mathematician Kazimierz Zarankiewicz, found a way of solving the problem with a drawing method (diag.), and a mathematical 'proof' - but the 'proof' was later found to contain errors. This led to the Zarankiewicz crossing number conjecture - which asks :

Can any complete bipartite graph be drawn with fewer crossings than the number given by Zarankiewicz?

More formally : It is always possible to draw the complete bipartite graph Km,n (a graph with m vertices on one side, n vertices on the other side, and mn edges connecting the two sides) with a number of crossings equal to :

$$ {\displaystyle \operatorname {cr} (K_{m,n})\leq {\biggl \lfloor }{\frac {n}{2}}{\biggr \rfloor }{\biggl \lfloor }{\frac {n-1}{2}}{\biggr \rfloor }{\biggl \lfloor }{\frac {m}{2}}{\biggr \rfloor }{\biggl \lfloor }{\frac {m-1}{2}}{\biggr \rfloor }.} $$

But is this always the minimum?

Although it's now been solved for some special cases, the general problem remains unsolved.

Further reading : Wolfram Mathworld

    Please share this page to help promote Wikenigma !

Dear reader : Do you have any suggestions for the site's content?

Ideas for new topics, and suggested additions / corrections for older ones, are always welcome.

If you have skills or interests in a particular field, and have suggestions for Wikenigma, get in touch !

Or, if you'd like to become a regular contributor . . . request a login password. Registered users can edit the entire content of the site, and also create new pages.

( The 'Notes for contributors' section in the main menu has further information and guidelines etc.)

Automatic Translation

You are currently viewing an auto-translated version of Wikenigma

Please be aware that no automatic translation engines are 100% accurate, and so the auto-translated content will very probably feature errors and omissions.

Nevertheless, Wikenigma hopes that the translated content will help to attract a wider global audience.

Show another (random) article

Further resources :