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Exact counting of Euler Tours for generalized series-parallel graphs
[article]

Prasad Chebolu, Mary Cryan, Russell Martin

2010
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arXiv
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pre-print

We give a simple polynomial-time algorithm to exactly *count* the number of *Euler* *Tours* (ETs) of any Eulerian generalized series-parallel *graph*, and show how to adapt this algorithm to exactly sample a random ...
Note that the class of generalized seriesparallel *graphs* includes all outerplanar *graphs*. We can perform the *counting* *in* time O(mΔ^3), where Δ is the maximum degree of the *graph* with m edges. ...
*In* fact, a recent result by Steve Noble [9] shows that (i),(ii) and (iii) could be *counted* exactly for a larger class of *graphs*, namely, the class of *bounded* *treewidth* *graphs*. ...

arXiv:1005.3477v1
fatcat:wcckfcxszndxnmumjaqi5nxqpa