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RSA
2006
66views more  RSA 2006»
15 years 10 days ago
Regular graphs whose subgraphs tend to be acyclic
Motivated by a problem that arises in the study of mirrored storage systems, we describe, for any fixed , > 0 and any integer d 2, explicit or randomized constructions of d-r...
Noga Alon, Eitan Bachmat
CPC
1998
154views more  CPC 1998»
15 years 2 days ago
Asymptotic Enumeration of Eulerian Circuits in the Complete Graph
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, ...
Brendan D. McKay, Robert W. Robinson
RSA
2011
126views more  RSA 2011»
14 years 7 months ago
Local resilience of almost spanning trees in random graphs
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically a...
József Balogh, Béla Csaba, Wojciech ...
CPC
2002
95views more  CPC 2002»
15 years 6 days ago
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, . . . ...
Catherine S. Greenhill, Svante Janson, Jeong Han K...
SODA
2012
ACM
213views Algorithms» more  SODA 2012»
13 years 2 months ago
Expanders are universal for the class of all spanning trees
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...