Expanding graphs contain all small trees
Combinatorica
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 large induced trees and long induced paths in sparse random graphs
Journal of Combinatorial Theory Series B
Subdivided graphs have linear Ramsey numbers
Journal of Graph Theory
Automorphism groups, isomorphism, reconstruction
Handbook of combinatorics (vol. 2)
Faster mixing via average conductance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal construction of edge-disjoint paths in random graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Finding long paths and cycles in sparse Hamiltonian graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Edge-Disjoint Paths in Expander Graphs
SIAM Journal on Computing
Random walks on the symmetric group generated by conjugacy classes
Random walks on the symmetric group generated by conjugacy classes
Tight Bounds for the Cover Time of Multiple Random Walks
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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We prove that regular graphs with large degree and small mixing time contain long paths and some other families of graphs as subgraphs. We present then an efficient algorithm for finding long paths. We apply the results to size Ramsey numbers and self-avoiding walks in graphs.