Combinatorica
Expanding graphs contain all small trees
Combinatorica
Universal graphs for bounded-degree trees and planar graphs
SIAM Journal on Discrete Mathematics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A small universal graph for bounded-degree planar graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
A proof of alon's second eigenvalue conjecture
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Optimal universal graphs with deterministic embedding
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On induced-universal graphs for the class of bounded-degree graphs
Information Processing Letters
Bandwidth, expansion, treewidth, separators and universality for bounded-degree graphs
European Journal of Combinatorics
Expanders are universal for the class of all spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An improved upper bound on the density of universal random graphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
SIAM Journal on Discrete Mathematics
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Let ℋ be a family of graphs. A graph T isℋ-universal if it contains a copy of eachHεℋ as a subgraph. Letℋ(k,n) denote the family of graphs on nvertices with maximum degree at most k. For all positiveintegers k and n, we construct anℋ(k,n)-universal graph T withOk(n2-2/klog4/kn)edges and exactly n vertices. The number of edges is almostas small as possible, as Ω(n2-2/k) is alower bound for the number of edges in any such graph. Theconstruction of T is explicit, whereas the proof ofuniversality is probabilistic and is based on a novel graphdecomposition result and on the properties of random walks onexpanders. © 2006 Wiley Periodicals, Inc. Random Struct. Alg.,2007