Permutation Pseudographs And Contiguity

The space of permutation pseudographs is a probabilistic model of 2-regular pseudographs on n vertices, where a pseudograph is produced by choosing a permutation of {1, 2, . . . , n} uniformly at random and taking the n edges {i, (i)}. We prove several contiguity results involving permutation pseudographs (contiguity is a kind of asymptotic equivalence of sequences of probability spaces). Namely, we show that a random 4-regular pseudograph is contiguous with the sum of two permutation pseudographs, the sum of a permutation pseudograph and a random Hamilton cycle, and the sum of a permutation pseudograph and a random 2-regular pseudograph. (The sum of two random pseudograph spaces is defined by choosing a pseudograph from each space independently and taking the union of the edges of the two pseudographs.) All these results are proved simultaneously by working in a general setting, where each cycle of the permutation is given a nonnegative constant multiplicative weight. A further cont...

• Type: Journal
• Year: 2002
• Where: CPC
• Authors: Catherine S. Greenhill, Svante Janson, Jeong Han Kim, Nicholas C. Wormald
• Keywords: CPC 2002, Permutation Pseudograph, Pseudograph, Random