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-1118 Oriented trees in n-chromatic digraphs
- Math-1119 Directed path of length twice the minimum outdegree
- Math-1120 Caccetta-Häggkvist Conjecture
- Math-1121 Long directed cycles in diregular digraphs
- Math-1122 Arc-disjoint out-branching and in-branching
- Math-1123 Hoàng-Reed Conjecture
- Math-1124 Arc-disjoint directed cycles in regular directed graphs
- Math-1125 Large acyclic induced subdigraph in a planar oriented graph.
- Math-1126 Monochromatic reachability or rainbow triangles
- Math-1127 Decomposing an even tournament in directed paths.
- Math-1128 Decomposing k-arc-strong tournament into k spanning strong digraphs
- Math-1129 Triangle-packing vs triangle edge-transversal.
- Math-1130 The Bollobás-Eldridge-Catlin Conjecture on graph packing
- Math-1131 Weak saturation of the cube in the clique
- Math-1132 Simultaneous partition of hypergraphs
- Math-1133 Turán's problem for hypergraphs
- Math-1134 Coloring random subgraphs
- Math-1135 Negative association in uniform forests
- Math-1136 Chromatic number of random lifts of complete graphs
- Math-1137 Domination in plane triangulations
- Math-1138 Large induced forest in a planar graph.
- Math-1139 Every 4-connected toroidal graph has a Hamilton cycle
- Math-1140 Degenerate colorings of planar graphs
- Math-1141 3-Colourability of Arrangements of Great Circles
- Math-1142 The Crossing Number of the Complete Graph
- Math-1143 The Crossing Number of the Complete Bipartite Graph
- Math-1144 Crossing numbers and coloring
- Math-1145 Are different notions of the crossing number the same?
- Math-1146 Universal point sets for planar graphs
- Math-1344 Exact colorings of graphs
- Math-1345 Obstacle number of planar graphs
- Math-1346 Switching reconstruction of digraphs
- Math-1347 Fractional Hadwiger
- Math-1348 3-Edge-Coloring Conjecture
- Math-1349 Triangle free strongly regular graphs
- Math-1350 Faithful cycle covers
- Math-1351 Decomposing eulerian graphs
- Math-1352 Geodesic cycles and Tutte's Theorem
- Math-1353 Random stable roommates
- Math-1354 Highly connected graphs with no K_n minor
- Math-1355 Forcing a $K_6$-minor
- Math-1356 Linial-Berge path partition duality
- Math-1357 Three-chromatic (0,2)-graphs
- Math-1358 Packing T-joins
- Math-1359 A generalization of Vizing's Theorem?
- Math-1360 List colorings of edge-critical graphs
- Math-1361 Universal Steiner triple systems
- Math-1362 Circular choosability of planar graphs
- Math-1363 Good Edge Labelings
- Math-1364 4-flow conjecture