The maximum number of copies of any hypergraph H in Berge-K_k-free r-graphs is achieved by the balanced complete (k-1)-partite r-graph for all sufficiently large k, with related bounds connecting hypergraph and graph cases.
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6 Pith papers cite this work. Polarity classification is still indexing.
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For any tree T and family F, ex(n,T,F) is either Ω(n^{k+1}) or O(ex(n,F)^k) for every integer k.
For prime power t and n = t^{2e-1}, ex(n, K_{t,t}, K_{2,t+1}) = (1 + o(1)) n² / (2t(t-1)).
Constructs K_{2,t+1}-free graphs with Ω_t(n^{2}) copies of K_{t,t}, proving ex(n, K_{t,t}, K_{2,t+1}) = Θ_t(n^{2}).
Admissible graphs admit strong majority edge-colorings with five colors, improving the prior upper bound of eight.
Investigates a prior conjecture on the extremal number of t-stars in non-k-edge-hamiltonian graphs for small t.
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Generalized Tur\'an problems for Berge hypergraphs
The maximum number of copies of any hypergraph H in Berge-K_k-free r-graphs is achieved by the balanced complete (k-1)-partite r-graph for all sufficiently large k, with related bounds connecting hypergraph and graph cases.
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Helly Theorems for Generalized Tur\'an Problems
For any tree T and family F, ex(n,T,F) is either Ω(n^{k+1}) or O(ex(n,F)^k) for every integer k.
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$K_{2, t+1}$-free graphs containing an optimal number of $K_{t, t}$'s
For prime power t and n = t^{2e-1}, ex(n, K_{t,t}, K_{2,t+1}) = (1 + o(1)) n² / (2t(t-1)).
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$K_{2,t+1}$-free graphs with many copies of $K_{t,t}$
Constructs K_{2,t+1}-free graphs with Ω_t(n^{2}) copies of K_{t,t}, proving ex(n, K_{t,t}, K_{2,t+1}) = Θ_t(n^{2}).
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Strong Majority Edge-Coloring
Admissible graphs admit strong majority edge-colorings with five colors, improving the prior upper bound of eight.
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Further Results on the maximun number of stars in graphs with forbidden properties
Investigates a prior conjecture on the extremal number of t-stars in non-k-edge-hamiltonian graphs for small t.