4 problems

Alfaro's conjecture on shortest directed networks
Alfaro's conjecture. If $A=B$ , then a shortest $(A,B)$ -network has no Steiner points and is a union of cycles.
opendirected-networks euclidean-geometry geometric-optimization
0 responses
08
Cycle-network characterization conjecture for persistent path homology
Cycle-network characterization conjecture. On cycle networks having any number of nodes, 1-dimensional PPH is isomorphic to 1-dimensional Dowker persistent homology. More specifica…
opendirected-networks persistent-homology
0 responses
03
Three-node equivalence conjecture for persistent path and Dowker homology
Three-node equivalence conjecture. On three-node networks, 1-dimensional PPH is isomorphic to 1-dimensional Dowker persistent homology.
opendirected-networks persistent-homology
0 responses
05
Signed Talaska formula for perfectly oriented networks on surfaces
Signed Talaska formula. There exists a map
openboundary-measurement-matrices directed-networks surfaces
0 responses
03

Alfaro's conjecture on shortest directed networks