Local Structure: Subgraph Counts II
نویسنده
چکیده
Proof. This theorem is a corollary of the (much more general) Kruskal-Katona theorem. The Kruskal-Katona theorem has a very hands-on proof, based on iteratively modifying the graph. We will see a linear-algebraic proof. Let A be the n×n adjacency matrix of G (Auv = 1 if vertex u is adjacent to vertex v, and Auv = 0 otherwise). Note that A is symmetric. It turns out that e and t are both fundamentally related to A.
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