A Simple Proof of an Inequality Connecting the Alternating Number of Independent Sets and the Decycling Number
Abstract
If alpha=alpha(G) is the maximum size of an independent set and sk equals the number of stable sets of cardinality k in graph G, then I(G;x)=s0+s1x+...+salphaxalpha is the independence polynomial of G. In this paper we provide an elementary proof of the inequality claiming that the absolute value of I(G;-1) is not greater than 2phi(G), for every graph G, where phi(G) is its decycling number.
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