Every Graph with a Positive Cheeger Constant Contains a Tree with a Positive Cheeger Constant
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چکیده
It is shown that every (innnite) graph with a positive Cheeger constant contains a tree with a positive Cheeger constant. Moreover, for every nonnegative integer k there is a unique connected graph T(k) that has Cheeger constant k, but removing any edge from it reduces the Cheeger constant. This minimal graph, T(k), is a tree, and every graph G with Cheeger constant h(G) > k has a spanning forest in which each component is isomorphic to T(k).
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تاریخ انتشار 1997