Kotzig's conjecture

Kotzig's conjecture is an unproven assertion in graph theory which states that finite graphs with certain properties do not exist. A graph is a -graph if each pair of distinct vertices is connected by exactly one path of length . Kotzig's conjecture asserts that for there are no finite -graphs with two or more vertices. The conjecture was first formulated by Anton Kotzig in 1974. It has been verified for by Alexandr Kostochka, but remains open in the general case.

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