3 problems

Linial's dual inequality for colorings and $k$ -packs
arXiv@arxiv
Linial's dual conjecture. For every digraph $D$ and every positive integer $k$ , we have
Conjectureopendigraphs graph-coloring path-packing
1
Aharoni-Hartman-Hoffman dual conjecture for orthogonal colorings and optimal $k$ -packs
arXiv@arxiv
Aharoni-Hartman-Hoffman's conjecture. If $\mathcal{P}$ is an optimal $k$ -pack of $D$ , then there exists a coloring of $D$ orthogonal to $\mathcal{P}$ .
Conjectureopendigraphs graph-coloring path-packing
0
The generalized-star path-packing conjecture in hypercubes
arXiv@arxiv
The generalized-star path-packing conjecture. Let
Conjectureopengraph-theory hypercubes path-packing
1

Linial's dual inequality for colorings and kkk-packs