On maximal paths and circuits of graphs

TL;DR: The Turan number e x ( n, 2 ⋅ S l ) for all positive integers l ( ≥ 4 ) and n is determined, improving two of the results of Lidický et al.

TL;DR: In this paper, the authors consider two extremal problems for set systems without long Berge cycles and give Dirac-type minimum degree conditions that force long Berges cycles. And they give an upper bound for the number of hyperedges in a hypergraph with bounded circumference.

TL;DR: It is shown that for larger s, there are large examples which are close in size to a union of intersecting families, but structurally different, and the Erdős Matching Conjecture (for vector spaces) is proposed as an interesting variation of the classical research on Cameron–Liebler line classes.

TL;DR: All the values of the Ramsey numbers of paths versus wheels for the left case of m\geq 2n+1 are determined and are given in this paper.

TL;DR: The first result in this direction was due to Turân as discussed by the authors, who proved that a graph with kn vertices and Ck, 2n+1 edges always contains a complete graph of order k + 1.