I. Benjamini, O.H aggstr om and E. Mossel (2000), On random graph homomorphisms into Z, J. Combin. Theory 78, 86-114.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in full generality is hard, but things get much easier if one focuses on the case when G is a tree. Brightwell and Winkler [2] make a thorough investigation of the case G = T r , the r 1 regular tree and H = K q and also give some answers for general H. We would also like to point out the paper [1] where one treats the case H = Z. Since Z is not a nite graph the problems are a bit di erent, but we shall take some inspiration from the methods of that paper. Brightwell and Winkler prove in the case G = T r and H = K q that one can always nd a set of activities for which there are multiple ....

....boundary con guration and p v (h) P v ( v) h) then p v (h) Z v h p v i (h ) 2.2) where Z v is the normalizing constant 0 h p v i (h ) Using (2. 2) one can recursively calculate p n (h) p o (h) These recursive expressions were observed for the case H = Z in [1], in which case they lead to a kind of generalized Pascal triangle, and for the case H = K q , the case that we are mainly interested in here, in [2] They easily generalize to the case of non uniform activities. Let us illustrate by an example with r = 2 and H = K 4 . Write p v for the ....

I. Benjamini, O.H aggstr om and E. Mossel (2000), On random graph homomorphisms into Z, J. Combin. Theory 78, 86-114.

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I. Benjamini, O. Haggstrom and E. Mossel, Random graph homomorphisms into Z, preprint (1998).

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I. Benjamini, O. Haggstrom and E. Mossel, Random graph homomorphisms into Z, preprint (1998).

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