Graph theory
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2209 List Hadwiger Conjecture
- Math-2252 Finiteness of a Shafarevich–Tate group needed by the lifting method
- Math-2330 Caccetta–Häggkvist Conjecture for Directed Triangles
- Math-2362 Forcing Graphs for Quasirandomness
- Math-2363 Forcing Conjecture for Bipartite Cyclic Graphs
- Math-2368 Hill Conjecture for Complete Graph Crossing Numbers
- Math-2388 Minimum Graph Homomorphism Counts at Fixed Density
- Math-2394 Sidorenko's Inequality for Bipartite Graphs
- Math-2395 Linear Cycle-and-Edge Decompositions of Graphs
- Math-2417 Color Savings and Strong Chromatic Index Bounds
- Math-2419 Stanley–Stembridge Chromatic Symmetric Function Conjecture
- Math-2443 Distances in Decorated Random Planar Maps
- Math-2452 Hadwiger’s Coloring Conjecture and Its Odd-Minor Variant
- Math-2472 Hadwiger’s Graph-Coloring Conjecture
- Math-2476 Erdős–Gallai Cycle-Decomposition Conjecture
- Math-2489 Chromatic Number of Overlapping Unit-Circle Constellations
- Math-2505 Bounded-Diameter Monochromatic Covers
- Math-3037 The Cycle Double Cover Conjecture
- Math-3097 Lovász Conjecture
- Math-3104 Brouwer's Conjecture on Graph Laplacians
- Math-3105 Eternal Domination vs Domination Number
- Math-3106 1-Factorization Conjecture
- Math-3107 Cereceda's Conjecture
- Math-3108 Jaeger's Petersen Coloring Conjecture
- Math-3109 List Coloring Conjecture
- Math-3110 Oberwolfach Problem
- Math-3111 Tuza's Conjecture
- Math-3112 Zarankiewicz Problem
- Math-3113 Characterization of Word-Representable Planar Graphs
- Math-3114 Word-Representable Graphs: Forbidden Subgraph Characterization
- Math-3115 Word-Representable Near-Triangulations
- Math-3116 Representation Number 3 Classification
- Math-3117 Crown Graphs and Longest Word-Representants
- Math-3118 Line Graphs of Non-Word-Representable Graphs
- Math-3119 Imbalance Conjecture
- Math-3120 Implicit Graph Conjecture
- Math-3121 Teschner's Bondage Number Conjecture
- Math-3122 Tutte's 4-Flow Conjecture for Petersen-Minor-Free Graphs
- Math-3309 Book Thickness of Subdivisions
- Math-3310 Number of Cliques in Minor-Closed Classes
- Math-3311 Shuffle-Exchange Conjecture (graph-theoretic form)
- Math-3312 Odd cycles and low oddness
- Math-3313 Beneš Conjecture (graph-theoretic form)
- Math-3314 Finding k-edge-outerplanar graph embeddings
- Math-3315 Vertex Coloring of graph fractional powers
- Math-3316 Matching cut and girth
- Math-3317 Turán number of a finite family.
- Math-3318 Chromatic Number of Common Graphs
- Math-3319 Circular flow numbers of $r$-graphs
- Math-3320 Monochromatic vertex colorings inherited from Perfect Matchings