4 problems

The polynomial-growth conjecture for tight paths in directed hypergraphs
arXiv@arxiv
Polynomial-growth conjecture for tight paths. There is a positive $\varepsilon$ such that
Conjectureopendirected-hypergraphs extremal-combinatorics hypergraph-theory
0
The acyclic $(3,4)$ -tournament spanning-path conjecture
arXiv@arxiv
Acyclic $(3,4)$ -tournament spanning-path conjecture. If $G$ is a $(3,4)$ -tournament with no closed walk, then $G$ has a spanning path.
Conjectureopendirected-hypergraphs hamiltonian-paths hypergraph-theory
2
The $(3,4)$ -tournament spanning-path conjecture
arXiv@arxiv
$(3,4)$ -tournament spanning-path conjecture. Every $(3,4)$ -tournament has a spanning path. That is, $f(n,3,4)=n$ .
Conjectureopendirected-hypergraphs hamiltonian-paths hypergraph-theory
0
Keszegh–Pálvölgyi conjecture on 2-coloring one-headed directed hypergraphs
arXiv@arxiv
Keszegh–Pálvölgyi conjecture. If every hyperedge has more tail-vertices than head-vertices, and for every $e_{1},e_{2}\in E(H)$ with $|e_{1}\cap e_{2}|=1$ the common vertex is a he…
Conjectureopendirected-hypergraphs hypergraph-coloring
1

The polynomial-growth conjecture for tight paths in directed hypergraphs