John

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seen May 7 '12 at 5:10

May
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awarded  Commentator
May
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comment Graph Theory - Spanning Trees
No worries, thank you so much for your assistance
May
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accepted Graph Theory - Spanning Trees
May
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comment Graph Theory - Spanning Trees
that helps a lot and i think I am at a general formula, but i have one question regarding what you added to your hint/answer. Should it be 4 * 5 instead of 4 * 6 since we have 4 of 5 edges to choose from c5 and 5 of 6 edges to choose from c6?
May
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awarded  Scholar
May
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comment Bijective Proof - partitions
Thank you! i appreciate your help
May
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accepted Bijective Proof - partitions
May
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comment Graph Theory - Spanning Trees
true, i apologize. I still can't gather a final formula / answer
May
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comment Bijective Proof - partitions
sorry that is the wrong link. The correct link is www-math.mit.edu/~rstan/bij.pdf and it is question 93.
May
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comment Graph Theory - Spanning Trees
I have broken the graph up into two parts, just as @Brian has done below. 1. Spanning trees of G that do not contain the shared edge and 2. Spanning trees of G that do contain the shared edge
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comment Graph Theory - Spanning Trees
case 2: ((x + y - 1) choose (x + y - 2)) ?
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comment Graph Theory - Spanning Trees
case 1: ((x + y) choose (x + y - 1)) ?
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comment Graph Theory - Spanning Trees
did you mean, you can remove any of the other x + y - 1 edges to get a spanning tree?
May
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comment Graph Theory - Spanning Trees
I have gone through drawing out all possibilities for some of the smaller cases, looking for a pattern. It may be and inclusion exclusion of choosing n edges from x.. but I can't come up with a formula.
May
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asked Bijective Proof - partitions
May
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asked Graph Theory - Spanning Trees