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Showing 1-6 of 6 problems

Difficulty Level

All LevelsL1: TractableL2: IntermediateL3: AdvancedL4: ExpertL5: Millennium Prize

Category

All CategoriesNumber TheoryCombinatoricsGraph TheoryAlgebraAlgebraic GeometryGeometryTopologyAnalysisPartial Differential EquationsSet TheoryComputer ScienceMathematical Physics

Problem Set

All SetsMillennium Prize ProblemsHilbert's 23 ProblemsBen Green's 100 Open ProblemsDARPA's 23 Mathematical ChallengesSmale's ProblemsLandau's Problems

Status

All StatusOpenSolved
GRAPH-004
Open

Erdős–Hajnal Conjecture

For any fixed graph $H$, do $H$-free graphs contain large cliques or independent sets?...

L5
Graph Theory
289
23
GRAPH-017
Open

GNRS Conjecture

Do minor-closed graph families have $\ell_1$ embeddings with bounded distortion?...

L5
Graph Theory
145
11
GRAPH-026
Open

Moore Graph Existence

Does a Moore graph with girth 5 and degree 57 exist?...

L5
Graph Theory
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
Graph Theory
234
19
GRAPH-056
Open

Tutte's 5-Flow Conjecture

Does every bridgeless graph have a nowhere-zero 5-flow?...

L5
Graph Theory
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
Graph Theory
198
16

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