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-3321 Laplacian Degrees of a Graph
- Math-3322 Cores of strongly regular graphs
- Math-3323 Complete bipartite subgraphs of perfect graphs
- Math-3324 Asymptotic Distribution of Form of Polyhedra
- Math-3325 Cycle double cover conjecture
- Math-3326 Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour.
- Math-3327 Every prism over a 3-connected planar graph is hamiltonian.
- Math-3328 Forcing a 2-regular minor
- Math-3329 Decomposing a connected graph into paths.
- Math-3330 Total Colouring Conjecture
- Math-3331 Seymour's r-graph conjecture
- Math-3332 Goldberg's conjecture
- Math-3333 Strong edge colouring conjecture
- Math-3334 Cores of Cayley graphs
- Math-3335 Weak pentagon problem
- Math-3336 Algorithm for graph homomorphisms
- Math-3337 Real roots of the flow polynomial
- Math-3338 Circular flow number of regular class 1 graphs
- Math-3339 Coloring the Odd Distance Graph
- Math-3340 Hedetniemi's Conjecture
- Math-3341 Double-critical graph conjecture
- Math-3342 Are vertex minor closed classes chi-bounded?
- Math-3343 Choice Number of k-Chromatic Graphs of Bounded Order
- Math-3344 Erdős–Faber–Lovász conjecture
- Math-3345 Antidirected trees in digraphs
- Math-3346 Subdivision of a transitive tournament in digraphs with large outdegree.
- Math-3347 Hamilton cycle in small d-diregular graphs
- Math-3348 Erdős-Posa property for long directed cycles
- Math-3349 Monochromatic reachability in arc-colored digraphs
- Math-3350 Edge-disjoint Hamilton cycles in highly strongly connected tournaments.
- Math-3351 Partitionning a tournament into k-strongly connected subtournaments.
- Math-3352 Extremal problem on the number of tree endomorphism
- Math-3353 Odd-cycle transversal in triangle-free graphs
- Math-3354 Multicolour Erdős--Hajnal Conjecture
- Math-3355 PTAS for feedback arc set in tournaments
- Math-3356 ¿Are critical k-forests tight?
- Math-3357 Seymour's self-minor conjecture
- Math-3358 Unions of triangle free graphs
- Math-3359 Universal highly arc transitive digraphs
- Math-3360 Unfriendly partitions
- Math-3361 Highly arc transitive two ended digraphs
- Math-3362 End-Devouring Rays
- Math-3363 Grunbaum's Conjecture
- Math-3364 The Crossing Number of the Hypercube
- Math-3365 What is the largest graph of positive curvature?
- Math-4005 Yao-Yao Graph a Spanner?
- Math-4065 Babai's problem
- Math-4092 O9 — Counting distinct prime factors
- Math-4093 O18b — Recognizing primitive roots randomly
- Math-4094 O22a — Discrete logarithms modulo a composite