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|Paper IPM / M / 16534||
In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a graph G, we define the invariant η(G) as the maximum size of a clique disjoint edge set in G. We show that the regularity of the binomial edge ideal of G is bounded above by η(G). This, in particular, settles a conjecture on the regularity of binomial edge ideals in full generality.
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