Extremal problems of double stars
Abstract
In a generalized Tur\'an problem, two graphs H and F are given and the question is the maximum number of copies of H in an F-free graph of order n. In this paper, we study the number of double stars Sk,l in triangle-free graphs. We also study an opposite version of this question: what is the maximum number edges/triangles in graphs with double star type restrictions, which leads us to study two questions related to the extremal number of triangles or edges in graphs with degree-sum constraints over adjacent or non-adjacent vertices.
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