Unsolved Problems
Showing 1-6 of 6 problems
Category
Problem Set
Status
GRAPH-004
Open
Erdős–Hajnal Conjecture
For any fixed graph $H$, do $H$-free graphs contain large cliques or independent sets?...
L5
289
23
GRAPH-017
Open
GNRS Conjecture
Do minor-closed graph families have $\ell_1$ embeddings with bounded distortion?...
L5
145
11
GRAPH-026
Open
Moore Graph Existence
Does a Moore graph with girth 5 and degree 57 exist?...
L5
223
18
GRAPH-031
Open
Erdős-Hajnal Conjecture
Does every graph family defined by a forbidden induced subgraph have polynomial-sized cliques or independent sets?...
L5
234
19
GRAPH-056
Open
Tutte's 5-Flow Conjecture
Does every bridgeless graph have a nowhere-zero 5-flow?...
L5
267
21
GRAPH-057
Open
Tutte's 4-Flow Conjecture for Petersen-Minor-Free Graphs
Does every Petersen-minor-free bridgeless graph have a nowhere-zero 4-flow?...
L5
198
16