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-881 Erdős Problem #629
- Math-884 Erdős Problem #640
- Math-885 Erdős Problem #642
- Math-886 Erdős Problem #643
- Math-887 Erdős Problem #644
- Math-893 Erdős Problem #668
- Math-909 Erdős Problem #701
- Math-910 Erdős Problem #704
- Math-911 Erdős Problem #706
- Math-916 Erdős Problem #719
- Math-925 Erdős Problem #761
- Math-926 Erdős Problem #766
- Math-932 Erdős Problem #778
- Math-940 Erdős Problem #802
- Math-941 Erdős Problem #805
- Math-942 Erdős Problem #809
- Math-943 Erdős Problem #810
- Math-944 Erdős Problem #811
- Math-976 Erdős Problem #901
- Math-977 Erdős Problem #902
- Math-978 Erdős Problem #911
- Math-981 Erdős Problem #917
- Math-982 Erdős Problem #918
- Math-983 Erdős Problem #919
- Math-1042 Pebbling a cartesian product
- Math-1043 Edge Reconstruction Conjecture
- Math-1044 Shannon capacity of the seven-cycle
- Math-1045 Star chromatic index of cubic graphs
- Math-1046 Star chromatic index of complete graphs
- Math-1047 Minimal graphs with a prescribed number of spanning trees
- Math-1048 The Borodin-Kostochka Conjecture
- Math-1049 Stable set meeting all longest directed paths.
- Math-1050 Arc-disjoint strongly connected spanning subdigraphs
- Math-1051 Do any three longest paths in a connected graph have a vertex in common?
- Math-1052 Lovász Path Removal Conjecture
- Math-1053 Switching reconstruction conjecture
- Math-1054 Signing a graph to have small magnitude eigenvalues
- Math-1055 Are almost all graphs determined by their spectrum?
- Math-1056 Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournament
- Math-1057 3-Decomposition Conjecture
- Math-1058 Cycle Double Covers Containing Predefined 2-Regular Subgraphs
- Math-1059 Sidorenko's Conjecture
- Math-1060 Chromatic number of $\frac{3}{3}$-power of graph
- Math-1061 57-regular Moore graph?
- Math-1062 Half-integral flow polynomial values
- Math-1063 Ramsey properties of Cayley graphs
- Math-1064 Does the chromatic symmetric function distinguish between trees?
- Math-1065 Graham's conjecture on tree reconstruction
- Math-1066 Nearly spanning regular subgraphs
- Math-1067 Domination in cubic graphs