Universal graphs for bounded-degree trees and planar graphs
SIAM Journal on Discrete Mathematics
An algorithmic version of the blow-up lemma
Random Structures & Algorithms
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Near-optimum Universal Graphs for Graphs with Bounded Degrees
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Spanning Subgraphs of Random Graphs
Combinatorics, Probability and Computing
Hypergraph Packing and Graph Embedding
Combinatorics, Probability and Computing
Random Structures & Algorithms
Sparse universal graphs for bounded-degree graphs
Random Structures & Algorithms
Optimal universal graphs with deterministic embedding
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Random Structures & Algorithms
Embedding nearly-spanning bounded degree trees
Combinatorica
An improved upper bound on the density of universal random graphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We prove that asymptotically (as $n\to\infty$) almost all graphs with $n$ vertices and $C_dn^{2-\frac{1}{2d}} \log^{\frac{1}{d}} n$ edges are universal with respect to the family of all graphs with maximum degree bounded by $d$. Moreover, we provide an efficient deterministic embedding algorithm for finding copies of bounded degree graphs in graphs satisfying certain pseudorandom properties. We also prove a counterpart result for random bipartite graphs, where the threshold number of edges is even smaller but the embedding is randomized.