Explicit expanders and the Ramanujan conjectures
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
SIAM Journal on Algebraic and Discrete Methods
Combinatorica
On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On the second eigenvalue of a graph
Discrete Mathematics
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
The expansion and mixing time of skip graphs with applications
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Novel architectures for P2P applications: The continuous-discrete approach
ACM Transactions on Algorithms (TALG)
Sparse universal graphs for bounded-degree graphs
Random Structures & Algorithms
Communication constraints in the average consensus problem
Automatica (Journal of IFAC)
On the design of hybrid peer-to-peer systems
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Revisiting the Efficiency of Malicious Two-Party Computation
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Expansion and Lack Thereof in Randomly Perturbed Graphs
Algorithms and Models for the Web-Graph
Vertex percolation on expander graphs
European Journal of Combinatorics
Rearrangeable and nonblocking [w, f] -distributors
IEEE/ACM Transactions on Networking (TON)
On Construction of Almost-Ramanujan Graphs
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Asymptotically optimal dynamic tree evolution by rapidly mixing random walks on regular networks
Journal of Parallel and Distributed Computing
Testing expansion in bounded-degree graphs
Combinatorics, Probability and Computing
A random walk model for infection on graphs: spread of epidemics & rumours with mobile agents
Discrete Event Dynamic Systems
Classical and quantum tensor product expanders
Quantum Information & Computation
Studies in complexity and cryptography
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
On the price of equivocation in byzantine agreement
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Sparse random graphs: Eigenvalues and eigenvectors
Random Structures & Algorithms
The time complexity of A* with approximate heuristics on multiple-solution search spaces
Journal of Artificial Intelligence Research
Analysis of accelerated gossip algorithms
Automatica (Journal of IFAC)
Hi-index | 0.01 |
A d-regular graph has largest or first (adjacency matrix) eigenvalue λ1 = d. In this paper we show the following conjecture of Alon. Fix an integer d 2 and a real ε 0. Then for sufficiently large n we have that "most" d-regular graphs on n vertices have all their eigenvalues except λ1 = d bounded above by 2√d-1 + ε. Our methods, being trace methods, also bound those eigenvalues below by -2√d-1 - ε.