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-1516 O34 — Solvability of the negative Pell equation
- Math-1517 O36 — Integer multiplication in linear bit complexity
- Math-1518 Conjecture 1.3 — Pillai
- Math-1519 Conjecture 1.9
- Math-1520 Conjecture 2.5 — Lang-Waldschmidt
- Math-1521 Conjecture 2.6
- Math-1522 Conjecture 2.14 — Mahler
- Math-1523 Conjecture 3.3 — Algebraic Independence of Logarithms of Algebraic Numbers
- Math-1524 Conjecture 3.5 — Strong Five Exponentials Conjecture
- Math-1525 Conjecture 3.6 — Roy
- Math-1526 Conjecture 3.8 — Gel’fond
- Math-1527 Conjecture 3.9 — Schneider
- Math-1528 Conjecture 3.10 — Gel’fond-Schneider
- Math-1529 Conjecture 3.15 — Goncharov
- Math-1530 Conjecture 3.16 — Zagier
- Math-1531 Conjecture 3.17
- Math-1532 Conjecture 3.18
- Math-1533 Conjecture 3.20 — Nesterenko
- Math-1534 Conjecture 4.1 — Lehmer's Problem
- Math-1535 Conjecture 4.3 — Amoroso-David
- Math-1536 Conjecture 4.11 — Wirsing and Schmidt
- Math-1653 Euclidean Minimum Spanning Tree
- Math-1657 Visibility Graph Recognition
- Math-1668 3D Minimum-Bend Orthogonal Graph Drawings
- Math-1707 Conjecture 0.1 — Is there an infinite expander?
- Math-1708 Nonamenable subgraphs of transitive graphs with exponential growth
- Math-1709 Nonamenable subgraphs under uniform exponential growth
- Math-1710 Cheeger constants of nets in transitive graphs
- Math-1711 Uniform expansion bounds for graph nets
- Math-1712 Grid-or-tree embeddings in superlinear Cayley graphs
- Math-1713 Roughly transitive graphs versus homogeneous spaces
- Math-1714 Minimum diameter realizing a prescribed local ball
- Math-1728 Liouville property of infinite Ramanujan graphs
- Math-1729 Liouville property under rough isometry to nonamenable Cayley graphs
- Math-1730 Liouville extensions by an isometric integer action
- Math-1733 Finite graphs whose every ball is an expander
- Math-1824 Some Questions — Question 6
- Math-1827 Some Questions — Question 13
- Math-1828 Some Questions — Question 17
- Math-1829 Some Questions — Question 29
- Math-1830 Some Questions — Question 32
- Math-1831 Some Questions — Question 33
- Math-1833 Some Questions — Question 42
- Math-2009 Some Questions — Question 7
- Math-2010 Some Questions — Question 8
- Math-2011 Some Questions — Question 12
- Math-2012 Some Questions — Question 16
- Math-2013 Some Questions — Question 23
- Math-2066 10 Lectures and 42 Open Problems — The planted clique problem
- Math-2208 Decomposing an eulerian graph into cycles.