6 problems

The correspondence coloring conjecture for $K_5$ -minor-free graphs
Correspondence coloring conjecture. The graph $G$ has $6$ disjoint $\mathbf{M}$ -colorings. Equivalently,
opencorrespondence-coloring graph-coloring minor-free-graphs
0 responses
04
Chen–Zhang's signless Laplacian extremal conjecture for $K_{s,t}$ -minor-free graphs
Chen–Zhang's conjecture.
openminor-free-graphs signless-laplacian spectral-graph-theory
0 responses
08
Class 1 conjecture for $K_5$ -minor free graphs of maximum degree six
Edge-coloring conjecture. Then $G$ is class $1$ .
openedge-coloring graph-coloring minor-free-graphs
0 responses
06
Signless Laplacian extremal conjecture for large $K_{s,t}$ -minor free graphs
Signless Laplacian extremal conjecture.
openminor-free-graphs signless-laplacian spectral-graph-theory
0 responses
05
Constant-congestion integrality-gap conjecture for maximum edge-disjoint paths in minor-closed families
Let ${\cal G}$ be any proper minor-closed family of graphs. The constant-congestion integrality-gap conjecture. The integrality gap of the flow LP for maximum edge-disjoint paths i…
opengraph-algorithms integrality-gaps minor-free-graphs
0 responses
04
The square-root query-complexity conjecture for testing H-minor freeness
Square-root query-complexity conjecture. For every $H$ , being $H$ -minor free can be tested with one-sided error using $\tilde{O}(\sqrt{n})$ queries, where $n$ is the number of vert…
openbounded-degree-graphs minor-free-graphs property-testing
0 responses
08

6 problems

The correspondence coloring conjecture for K5K_5K5​-minor-free graphs

Chen–Zhang's signless Laplacian extremal conjecture for Ks,tK_{s,t}Ks,t​-minor-free graphs

Class 1 conjecture for K5K_5K5​-minor free graphs of maximum degree six

Signless Laplacian extremal conjecture for large Ks,tK_{s,t}Ks,t​-minor free graphs

Constant-congestion integrality-gap conjecture for maximum edge-disjoint paths in minor-closed families

The square-root query-complexity conjecture for testing H-minor freeness

The correspondence coloring conjecture for $K_5$ -minor-free graphs

Chen–Zhang's signless Laplacian extremal conjecture for $K_{s,t}$ -minor-free graphs

Class 1 conjecture for $K_5$ -minor free graphs of maximum degree six

Signless Laplacian extremal conjecture for large $K_{s,t}$ -minor free graphs