We determine the asymptotic behaviour of the number of eulerian circuits in a complete graph of odd order. One corollary of our result is the following. If a maximum random walk, ...
A transition system T of an Eulerian graph G is a family of partitions of the edges incident to each vertex of G into transitions i.e. subsets of size two. A circuit decomposition...
Until now, the enumeration of connected graphs has been dealt with by probabilistic methods, by special combinatorial decompositions or by somewhat indirect formal series manipula...