Generalized Turán problems for double stars

Some Exact Results for Non-Degenerate Generalized Turán Problems

“…We remark that (i) is a straightforward extension of a proposition from [12], which states the same result with weakly F -Turán-good instead of weakly F -Turán-stable. Observe that in (ii), if F = K 3 , then we just add leaves to the endpoints of an edge.…”

“…In this paper we extend this result by going beyond (χ(F ) − 1)-partite graphs: we obtain exact results when the extremal construction is obtained by adding further edges to a complete (χ(F ) − 1)-partite graph. One such result has been obtained by Gerbner and Patkós [17]. Let B r,1 denote the graph consisting of two copies of K r sharing a vertex.…”

“…This approach where we prove that H is F -Turán-stable and use it to prove that H is F -Turán-good can also be found in [20,23,19,12]. Finally, Gerbner [14] provided the following general formulation.…”

“…It was shown in [4] that among B r,1 -free graphs, the most edges are contained in the Turán graph plus an additional edge. It was extended in [17] to any K r with r < k in place of K 2 . There are further results when B 3,1 is forbidden in [12].…”

“…It was extended in [17] to any K r with r < k in place of K 2 . There are further results when B 3,1 is forbidden in [12].…”