Optimal induced universal graphs for bounded-degree graphs
نویسندگان
چکیده
منابع مشابه
Near-Optimal Induced Universal Graphs for Bounded Degree Graphs
A graph U is an induced universal graph for a family F of graphs if every graph in F is a vertex-induced subgraph of U . For the family of all undirected graphs on n vertices Alstrup, Kaplan, Thorup, and Zwick [STOC 2015] give an induced universal graph with O ( 2n/2 ) vertices, matching a lower bound by Moon [Proc. of Glasgow Math. Association 1965]. Let k = dD/2e. Improving asymptotically on ...
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We show that for any constant ∆ ≥ 2, there exists a graph Γ with O(n) vertices which contains every n-vertex graph with maximum degree ∆ as an induced subgraph. For odd ∆ this significantly improves the best-known earlier bound of Esperet et al. and is optimal up to a constant factor, as it is known that any such graph must have at least Ω(n) vertices. Our proof builds on the approach of Alon a...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2017
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004117000706