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-1068 Friendly partitions
- Math-1069 Subgraph of large average degree and large girth.
- Math-1070 Partitioning edge-connectivity
- Math-1071 Kriesell's Conjecture
- Math-1072 The circular embedding conjecture
- Math-1073 (m,n)-cycle covers
- Math-1074 r-regular graphs are not uniquely hamiltonian.
- Math-1075 Hamiltonian cycles in line graphs
- Math-1076 Jones' conjecture
- Math-1077 Chords of longest cycles
- Math-1078 Hamiltonicity of Cayley graphs
- Math-1079 Strong 5-cycle double cover conjecture
- Math-1080 4-connected graphs are not uniquely hamiltonian
- Math-1081 Hamilton decomposition of prisms over 3-connected cubic planar graphs
- Math-1082 The Berge-Fulkerson conjecture
- Math-1083 The intersection of two perfect matchings
- Math-1084 Matchings extend to Hamiltonian cycles in hypercubes
- Math-1085 Jorgensen's Conjecture
- Math-1086 Seagull problem
- Math-1087 Partition of a cubic 3-connected graphs into paths of length 2.
- Math-1088 4-regular 4-chromatic graphs of high girth
- Math-1089 Coloring the union of degenerate graphs
- Math-1090 List Total Colouring Conjecture
- Math-1091 Petersen coloring conjecture
- Math-1092 Acyclic edge-colouring
- Math-1093 Edge list coloring conjecture
- Math-1094 Pentagon problem
- Math-1095 Mapping planar graphs to odd cycles
- Math-1096 5-flow conjecture
- Math-1097 Jaeger's modular orientation conjecture
- Math-1098 Bouchet's 6-flow conjecture
- Math-1099 The three 4-flows conjecture
- Math-1100 Strong colorability
- Math-1101 Reed's omega, delta, and chi conjecture
- Math-1102 Partial List Coloring
- Math-1103 Partial List Coloring
- Math-1104 Bounding the chromatic number of triangle-free graphs with fixed maximum degree
- Math-1105 Graphs with a forbidden induced tree are chi-bounded
- Math-1106 Acyclic list colouring of planar graphs.
- Math-1107 List chromatic number and maximum degree of bipartite graphs
- Math-1108 Colouring the square of a planar graph
- Math-1109 Bounding the on-line choice number in terms of the choice number
- Math-1110 Choosability of Graph Powers
- Math-1111 2-colouring a graph without a monochromatic maximum clique
- Math-1112 List Colourings of Complete Multipartite Graphs with 2 Big Parts
- Math-1113 Cycles in Graphs of Large Chromatic Number
- Math-1114 The Two Color Conjecture
- Math-1115 The Bermond-Thomassen Conjecture
- Math-1116 Seymour's Second Neighbourhood Conjecture
- Math-1117 Non-edges vs. feedback edge sets in digraphs