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SODA
2012
ACM

Expanders are universal for the class of all spanning trees

12 years 1 months ago
Expanders are universal for the class of all spanning trees
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs for various families F has received a considerable amount of attention. One is particularly interested in tight F-universal graphs, i. e., graphs whose number of vertices is equal to the largest number of vertices in a graph from F. Arguably, the most studied case is that when F is some class of trees. Given integers n and ∆, we denote by T (n, ∆) the class of all n-vertex trees with maximum degree at most ∆. In this work, we show that every n-vertex graph satisfying certain natural expansion properties is T (n, ∆)-universal or, in other words, contains every spanning tree of maximum degree at most ∆. Our methods also apply to the case when ∆ is some function of n. The result has a few very interesting implications. Most importantly, since random graphs are known to be good expanders, we obtain th...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where SODA
Authors Daniel Johannsen, Michael Krivelevich, Wojciech Samotij
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