Proof: Vertices of Strong Tournament Lie on Triangles | Graph Theory

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We prove that every vertex of a strongly connected tournament graph lie on a triangle (a 3-cycle). #GraphTheory

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Комментарии
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It helped me to notice that the sets { v }, U, W form a partition. Thus there is no vertices set X containing vertices outside [ v }, U, W. When travelling from v to a vertex w in W, we go from v to a vertex u in U. It must be possible to travel from u to w. We could firstly travel within U. Finally a bridge between U and W must exists because going back to v is of no use and there is no vertex x in a set X that would permit a longer path.

alexandrebailly
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Strong tournament lie? More like "Super great videos, with a learning value that's high!"

PunmasterSTP
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Great explanation but how many triangle in oriented complete graph ( tournaments)?

urgirlkayann