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Omni-MATH / There are n>2022 cities in the country. Some pairs of cities are connected with straight two-ways airlines. Call the set of the cities …A, B, C with the airlines AB, AC and BC of t…

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problem

There are n>2022n > 2022 cities in the country. Some pairs of cities are connected with straight two-ways airlines. Call the set of the cities {\it unlucky}, if it is impossible to color the airlines between them in two colors without monochromatic triangle (i.e. three cities AA, BB, CC with the airlines ABAB, ACAC and BCBC of the same color). The set containing all the cities is unlucky. Is there always an unlucky set containing exactly 2022 cities?
Plain-text mathematical notation (without MathML)
There are n>2022 cities in the country. Some pairs of cities are connected with straight two-ways airlines. Call the set of the cities {\it unlucky}, if it is impossible to color the airlines between them in two colors without monochromatic triangle (i.e. three cities A, B, C with the airlines AB, AC and BC of the same color). 

The set containing all the cities is unlucky. Is there always an unlucky set containing exactly 2022 cities?
Original LaTeX notation
There are $n > 2022$ cities in the country. Some pairs of cities are connected with straight two-ways airlines. Call the set of the cities {\it unlucky}, if it is impossible to color the airlines between them in two colors without monochromatic triangle (i.e. three cities $A$, $B$, $C$ with the airlines $AB$, $AC$ and $BC$ of the same color). 

The set containing all the cities is unlucky. Is there always an unlucky set containing exactly 2022 cities?

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Source and history

task_id
89bd5311-9511-5c96-a5c6-6f9d592c4a55
task_key
test--89bd5311-9511-5c96-a5c6-6f9d592c4a55
task_revision_id
1
config / split
/ test

Official source

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