4 problems

Halmos' reducible-operator conjecture for separable factors
arXiv@arxiv
Let $\mathcal{M}$ be a separable factor. An operator $T\in\mathcal{M}$ is reducible if there is a projection $P\in\mathcal{M}$ with $P\ne 0,I$ and $PT=TP$ . Halmos' conjecture. The…
Conjectureopenfactor-theory operator-algebras von-neumann-algebras
0
Conjecture on edge-disjoint 1-factors in realizations of degree sequences
arXiv@arxiv
Edge-disjoint 1-factor conjecture. Some realization of $\mathrm{\pi}$ has $k$ edge-disjoint $1$ -factors if and only if
Conjectureopendegree-sequences factor-theory graph-realizations
1
Anti-directed 2-factor conjecture for dense directed graphs
arXiv@arxiv
Anti-directed 2-factor conjecture. If
Conjectureopendirected-graphs factor-theory
0
Conjecture on 3-regular 2-factor hamiltonian bipartite graphs
arXiv@arxiv
A $2$ --factor hamiltonian graph is a graph whose every $2$ --factor is a Hamilton circuit. Consider the family of $3$ --regular $2$ --factor hamiltonian bipartite graphs constructed f…
Conjectureopenbipartite-graphs factor-theory graph-theory
0

Halmos' reducible-operator conjecture for separable factors