The Number of Independent Sets in a Regular Graph
نویسنده
چکیده
We show that the number of independent sets in an N -vertex, d-regular graph is at most (2−1), where the bound is sharp for a disjoint union of complete d-regular bipartite graphs. This settles a conjecture of Alon in 1991 and Kahn in 2001. Kahn proved the bound when the graph is assumed to be bipartite. We give a short proof that reduces the general case to the bipartite case. Our method also works for a weighted generalization, i.e., an upper bound for the independence polynomial of a regular graph.
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 19 شماره
صفحات -
تاریخ انتشار 2010