All Questions
5 questions
4
votes
1
answer
136
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Longest paths and cycles in Steiner triple systems
A Steiner triple system is a 3-uniform hypergraph in which every pair of vertices is contained in exactly one edge. A linear cycle (also called loose cycle) length $t$ consists
of $2t$ cyclically ...
- 373
2
votes
1
answer
131
views
Turán density of hypergraphs with very few edges
As usual, for an $r$-uniform hypergraph $G$, denote by $ex_r(n,G)$ the maximum number of edges an $r$-uniform, $G$-free hypergraph on $n$ vertices can have, and let $\lim \frac{ex_r(n,G)}{\binom nr}\...
- 19.1k
11
votes
0
answers
195
views
Number of triangle-free graphs with prescribed number of edges
This question is posted from StackExchange since it received no answer there.
Let $f(n, e)$ be the number of triangle-free graphs on $n$ vertices and $e$ edges. From empirical evidence, I am motivated ...
- 384
2
votes
1
answer
210
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3-uniform tetrahedron-free hypergraph on seven vertices
My problem concerns 3-uniform hypergraphs. Let $f(n)$ be the maximal number of edges in a 3-uniform hypergraph such that no four edges form a "tetrahedron", i.e., four edges that join the ...
- 2,811
6
votes
0
answers
889
views
Cliques of hyperedges
Suppose we have a graph, with multiple edges allowed. An edge-clique is a set $C$ of edges so that every two edges in $C$ share at least one endpoint. Note that any edge-clique falls into one of two ...
- 1,288