One vertex can be removed from the vertex set, V(T), of a strong tournament, T, so long as |V(T)| is greater than or equal to 4. Any strong tournament has (at least) one Hamilton for every k, where k is a set of natural numbers greater than or equal to 3 and lesser than or equal to n, where n = |V(T)|. Therefore, a n- 1 strong graph exists because an n - 1 Hamilton cycle exists where one vertex can be excluded. But how can I prove that T can have more than one vertex that is not critical (T-x and T-y are both strong)?
2026-03-26 12:50:41.1774529441
Can it be proven that more than one vertex can individually be removed from a strong tournament and still be strong?
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