Prove that any minimum vertex cover of a clique of size n must have exactly n-1 vertices

Question

How to prove that any minimum vertex cover of a clique of size n must have exactly n-1 vertices? THx

This question appears to be off-topic because it is graph theory rather than a concrete programming or implementation question — talonmies, Apr 18 '14 at 15:22
This question appears to be off-topic because it is should be asked on http://cs.stackexchange.com/ — Basile Starynkevitch, Apr 18 '14 at 15:22
This question appears to be off-topic because it shows no effort whatsoever, and reeks of homework. — LittleBobbyTables - Au Revoir, Apr 18 '14 at 15:26

score 0 · Accepted Answer · answered Apr 18 '14 at 15:34

0

If there's two vertices from the clique not in a set, then the edge between them isn't covered, so any cover must have at least n-1 vertices. Any subset of n-1 vertices is a cover, trivially.

answered Apr 18 '14 at 15:34

Paul Hankin

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Prove that any minimum vertex cover of a clique of size n must have exactly n-1 vertices

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