Comments on: A little (combinatorial) graph problem http://www.tangentspace.net/cz/archives/2008/07/a-little-combinatorial-graph-problem/ somewhere near the beginning. Fri, 21 Nov 2008 20:52:54 +0000 http://wordpress.org/?v=2.5 By: Alex http://www.tangentspace.net/cz/archives/2008/07/a-little-combinatorial-graph-problem/#comment-392162 Alex Tue, 15 Jul 2008 00:28:19 +0000 http://www.tangentspace.net/cz/?p=940#comment-392162 Oh. Thanks :P Oh. Thanks :P

]]> By: Pete http://www.tangentspace.net/cz/archives/2008/07/a-little-combinatorial-graph-problem/#comment-391987 Pete Mon, 14 Jul 2008 21:01:44 +0000 http://www.tangentspace.net/cz/?p=940#comment-391987 As stated, the LHS is a vector, which you're saying is equal to the number k. nk is the total number of vertex-edge pairs, which must be even since each edge touches 2 vertices. Or another way to look at it, it's the number of nonzeros in the incidence matrix, which must be even since it's symmetric hollow. As stated, the LHS is a vector, which you’re saying is equal to the number k.

nk is the total number of vertex-edge pairs, which must be even since each edge touches 2 vertices. Or another way to look at it, it’s the number of nonzeros in the incidence matrix, which must be even since it’s symmetric hollow.

]]> By: Alex http://www.tangentspace.net/cz/archives/2008/07/a-little-combinatorial-graph-problem/#comment-391974 Alex Mon, 14 Jul 2008 20:47:11 +0000 http://www.tangentspace.net/cz/?p=940#comment-391974 heh, circulant matrices work, true. The LHS isn't a sum. So, why won't it work if nk is odd? heh, circulant matrices work, true. The LHS isn’t a sum. So, why won’t it work if nk is odd?

]]> By: Pete http://www.tangentspace.net/cz/archives/2008/07/a-little-combinatorial-graph-problem/#comment-391908 Pete Mon, 14 Jul 2008 19:12:10 +0000 http://www.tangentspace.net/cz/?p=940#comment-391908 Nice warm up to start the day. At noon. The answer is any n greater than k, provided nk is even. It's pretty easy to construct example graphs with circulant connectivity matrices. BTW, you forgot to sum the LHS of your equation. =D Nice warm up to start the day. At noon.

The answer is any n greater than k, provided nk is even. It’s pretty easy to construct example graphs with circulant connectivity matrices.

BTW, you forgot to sum the LHS of your equation. =D

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