Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
Propagation connectivity of random hypergraphs
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
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We show that r-uniform hypertrees can be encoded in linear time using as little as n–2 integers in the range [1,n]. The decoding algorithm also runs in linear time. For general hypertrees, we require codes of length n+e–2, where e is the number of hyperedges. We show that there are at most $\frac {n^{(n-2)}-f(n,r)}{(r-1)^{(r-2)*\frac{n-1}{r-1}}}$ distinct labeled r-uniform hypertrees, where f(n,r) is a lower bound on the number of trees with vertex degrees exceeding $(r-1)+\frac {n-1}{r-1}-2$. We suggest a counting scheme for determining f(n,r).