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Destroyer of the roads

Source: St Petersburg Olympiad 2018, Grade 10, P1

June 22, 2018
combinatoricsgraph theory

Problem Statement

Misha came to country with nn cities, and every 22 cities are connected by the road. Misha want visit some cities, but he doesn`t visit one city two time. Every time, when Misha goes from city AA to city BB, president of country destroy kk roads from city BB(president can`t destroy road, where Misha goes). What maximal number of cities Misha can visit, no matter how president does?