TY - GEN
T1 - Optimal universal graphs with deterministic embedding
AU - Alon, Noga
AU - Capalbo, Michael
PY - 2008
Y1 - 2008
N2 - Let H be a finite family of graphs. A graph G is Huniversal if it contains a copy of each H ∈ H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For all admissible k and n, we construct an H(k, n)-universal graph G with at most Ck n2-2/k edges, where Ck is a constant depending only on k. This is optimal, up to the constant factor ck, as it is known that c′k,n22/k is a lower bound for the number of edges in any such graph. The construction of G is explicit, and there is an efficient deterministic algorithm for finding a copy of any given H ∈ H(k, n) in G.
AB - Let H be a finite family of graphs. A graph G is Huniversal if it contains a copy of each H ∈ H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For all admissible k and n, we construct an H(k, n)-universal graph G with at most Ck n2-2/k edges, where Ck is a constant depending only on k. This is optimal, up to the constant factor ck, as it is known that c′k,n22/k is a lower bound for the number of edges in any such graph. The construction of G is explicit, and there is an efficient deterministic algorithm for finding a copy of any given H ∈ H(k, n) in G.
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M3 - Conference contribution
AN - SCOPUS:58649088470
SN - 9780898716474
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 373
EP - 378
BT - Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
PB - Association for Computing Machinery
T2 - 19th Annual ACM-SIAM Symposium on Discrete Algorithms
Y2 - 20 January 2008 through 22 January 2008
ER -