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Tutte Polynomial Blocks

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Little

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Apr 15, 2006, 11:53:04 PM4/15/06
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Could someone please help me solve this problem:

T(G; x; y) is multiplicative over blocks; that is, if G has blocks B1,
. . . ,Bb, then

T(G; x; y) =
b
pi T(Bi, x, y)
i=1


These are a few examples that I could come up with:

G
1. nK1 = ¹Kn where 'K is the complement of K
2. Any tree
3. m loops
4. Cm
5. m jj edges

T(G, x, y)
1. 1
2. x^m
3. y^m
4. y+x+x^2+. . .+x^(m-1)
5. x+y+y^2+. . .+y^(m-1)

Little

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Apr 16, 2006, 7:52:05 PM4/16/06
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Could someone please help me by getting started on a proof for this
question. I am not sure where to start. Your help will greatly be
appreciated.

Proginoskes

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Apr 17, 2006, 1:30:21 AM4/17/06
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The actual problem would be nice.

If you're replying to a previous post, you should quote it. If you're
using Google Groups, don't click on the Reply link at the bottom of the
post; click on the More Options link at the top, then click on "Reply"
in the "menu" that pops up. The message will be posted.

Now: If you're asking how the Tutte Polynomial behaves with respect to
blocks, use the definition, assume you have a cut-vertex v in your
graph G, and go from there.

--- Christopher Heckman

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