Ervin Győri

The maximum number of triangles in c2k+1-free graphs

Upper and lower bounds are proved for the maximum number of triangles in C2k+1-free graphs. The bounds involve extremal numbers related to appropriate even cycles.

3-uniform hypergraphs avoiding a given odd cycle

We give upper bounds for the size of 3-uniform hypergraphs avoiding a given odd cycle using the definition of a cycle due to Berge. In particular, we show that a 3-uniform hypergraph containing no cycle of length 2k+1 has less than 4k4n1+1/k+O(n) edges. Constructions show that these bounds are best possible (up to constant factor) for k=1,2,3, 5.

Hypergraph Extensions of the Erdős-Gallai Theorem

Abstract The Erdős-Gallai Theorem gives the maximum number of edges in a graph without a path of length k. We extend this result for Berge paths in r-uniform hypergraphs. We also find the extremal hypergraphs avoiding t-tight paths of a given length and consider this extremal problem for other definitions of paths in hypergraphs.

On the maximum size of connected hypergraphs without a path of given length

In this note we asymptotically determine the maximum number of hyperedges possible in an

Constructions for the Optimal Pebbling of Grids

r

Hypergraphs with no odd cycle of given length

-uniform, connected

A note on the maximum number of triangles in a C 5 -free graph

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On the Turán number of some ordered even cycles

-vertex hypergraph without a Berge path of length

Hypergraphs with no cycle of a given length

k

Toward Żak's conjecture on graph packing

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