This is really bugging me, how do I prove this theorem?
The minimum number of vertices to connect n edges is n-1 (we're talking Euler and Hamiltonian circuits from discrete math).
Sorry, got it backwards. It should read: The minimum number of edges to connect n vertices is n-1.
Steve
Favorite Answer
If the vertices are numbered 1,2,3....n you don't have an edge until you get to #2, and you're done when the last edge hits #n. Since #1 isn't in the count for edges, they will number one less than the vertices.
All this is true only if #1 and #n are non-coincident.
elve_r
Start with the fact that if you take one edge and want to connect it to all others, that would be n-1 edges
bulman
The assertion of the theorem became into got here upon on a Babylonian pill circa 1900-1600 B.C. whether Pythagoras (c.560-c.480 B.C.) or somebody else from his college became into the 1st to discover its info can't be claimed with any degree of credibility. Euclid's (c 3 hundred B.C.) factors supply the 1st and, later, the same old reference in Geometry.
Anonymous
a