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Showing 1-6 of 6 problems

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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 ProblemsHardy-Littlewood ConjecturesErdős ProblemsRichard Guy - A: Prime Numbers
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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