An algorithm for finding Hamilton paths and cycles in random graphs
Combinatorica - Theory of Computing
Explicit construction of linear sized tolerant networks
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
On the second eigenvalue of a graph
Discrete Mathematics
Hereditary Extended Properties, Quasi-Random Graphs and Induced Subgraphs
Combinatorics, Probability and Computing
On packing Hamilton cycles in ε-regular graphs
Journal of Combinatorial Theory Series B
On fractional K-factors of random graphs
Random Structures & Algorithms
Expanders are universal for the class of all spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Given an r-regular graph G on n vertices with a Hamilton cycle, order its edges randomly and insert them one by one according to the chosen order, starting from the empty graph. We prove that if the eigenvalue of the adjacency matrix of G with the second largest absolute value satisfies λ = o(r5/2/(n3/2(logn)3/2)),then for almost all orderings of the edges of G at the very moment τ* when all degrees of the obtained random subgraph Hτ* of G become at least two, Hτ* has a Hamilton cycle. As a consequence we derive the value of the threshold for the appearance of a Hamilton cycle in a random subgraph of a pseudo-random graph G, satisfying the above stated condition.