59 What are the implications of the new quasi-polynomial time solution for the Graph Isomorphism problem? 2015-11-12T16:48:43.250

54 Which graphs are Cayley graphs? 2010-02-09T23:14:06.093

53 What is a continuous path? 2011-11-12T21:02:14.747

51 What is a chess piece mathematically? 2017-12-07T11:48:22.047

50 Connectivity of the Erdős–Rényi random graph 2011-03-30T14:50:37.210

48 Why are there 1024 Hamiltonian cycles on an icosahedron? 2010-09-05T12:07:00.357

48 Generalizations of the Four-Color theorem 2014-12-07T07:53:38.170

47 Do there exist chess positions that require exponentially many moves to reach? 2010-06-12T16:39:43.247

44 History of the four-colour problem 2012-01-12T11:38:08.327

42 Why are planar graphs so exceptional? 2009-11-29T07:35:48.643

40 Does every triangle-free graph with maximum degree at most 6 have a 5-colouring? 2010-09-06T19:58:11.410

39 Is it easy to produce hard-to-color graphs? 2014-05-30T13:26:47.083

38 Strengthening the Induction Hypothesis 2010-07-13T13:01:34.113

38 What is the sandpile torsor? 2011-12-15T19:08:55.877

37 Linear Algebra Proofs in Combinatorics? 2010-03-03T20:39:42.597

36 Algebraic Proof of 4-Colour Theorem? 2010-03-24T21:59:25.403

36 Good programs for drawing graphs ( directed weighted graphs ) 2011-02-12T12:56:33.847

34 Generalizations of Planar Graphs 2009-12-03T09:21:45.290

32 What are the Applications of Hypergraphs 2010-02-01T23:47:10.023

32 A conjecture on planar graphs 2017-07-04T17:27:39.607

31 Spectral graph theory: Interpretability of eigenvalues and -vectors 2010-05-17T08:09:00.107

31 Graph containing all trees? 2011-02-03T13:16:08.780

31 Why is "P vs. NP" necessarily relevant? 2011-02-03T21:04:02.657

31 How large is TREE(3)? 2012-04-12T06:35:54.440

31 3-colorings of the unit distance graph of $\Bbb R^3$ 2015-04-14T05:05:59.393

31 What does this connection between Chebyshev, Ramanujan, Ihara and Riemann mean? 2015-11-25T21:28:15.253

30 An edge partitioning problem on cubic graphs 2010-10-26T15:50:51.610

30 Can assignment solve stable marriage? 2010-11-12T15:04:39.600

30 Interesting and Accessible Topics in Graph Theory 2011-05-10T02:43:58.073

30 How much linear algebra can be done with graphs? 2011-06-17T23:30:54.990

30 Does every bipartite graph with 512 edges have an induced subgraph with 256 edges? 2012-11-06T21:14:08.837

30 Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power 2015-03-11T11:55:11.987

29 Bringing Number and Graph Theory Together: A Conjecture on Prime Numbers 2010-03-23T00:50:42.693

29 Is there a "knot theory" for graphs? 2011-10-30T00:46:32.147

29 Should axiomatic set theory be translated into graph theory? 2016-01-06T08:10:40.483

28 How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.? 2010-04-13T21:57:07.813

27 Applications of infinite graph theory 2010-09-22T19:39:37.003

27 Adjacency matrices of graphs 2011-01-15T16:32:50.763

27 Does this knot invariant distinguish trefoil chiralities? 2012-04-30T12:59:34.327

27 Is the empty graph a tree? 2013-02-01T19:33:47.210

27 Is this graph polynomial known? Can it be efficiently computed? 2014-07-26T04:54:51.953

26 A small unavoidable collection of subgraphs 2014-05-13T21:31:11.583

25 Is the Rado graph a Cayley graph? If so, what is the group like? (And other questions...) 2010-10-25T19:10:27.093

25 What is this subgroup of $\mathfrak S_{12}$? 2010-11-12T16:30:56.990

25 An unfair marriage lemma 2015-04-23T18:14:04.180

25 Algebraic proof of Five-Color Theorem using chromatic polynomials by Birkhoff and Lewis in 1946 2015-05-11T10:30:43.293

24 Disjoint stable sets in tournaments 2009-12-17T15:09:18.230

24 Who wins this two-player game based on the sandpile model? 2010-07-02T01:03:27.530

24 Removal of non-isomorphic edges results in the same graph 2014-07-15T17:44:06.337

24 What (fun) results in graph theory should undergraduates learn? 2016-02-06T08:33:57.580

23 Counting subgraphs of bipartite graphs 2010-01-19T13:55:44.760

23 Some models for random graphs that I am curious about 2010-05-23T17:02:49.170

23 Shortest grid-graph paths with random diagonal shortcuts 2010-11-13T14:01:13.760

23 Planar minor graphs 2012-03-27T23:28:06.810

23 Rock-paper-scissors... 2012-04-10T15:17:29.130

23 Determinants in Graph Theory 2013-06-27T03:43:52.797

23 Is every positive integer the permanent of some 0-1 matrix? 2017-08-29T17:24:42.887

22 Representability of finite metric spaces 2010-01-20T07:44:31.503

22 Monochromatic triangles in every two-coloring of the plane? 2010-07-29T19:20:29.440

22 Is there a 7-regular graph on 50 vertices with girth 5? What about 57-regular on 3250 vertices? 2010-10-28T01:42:09.990

22 What relationship, if any, is there between the diameter of the Cayley graph and the average distance between group elements? 2011-04-12T18:35:49.423

22 The Matrix-Tree Theorem without the matrix 2011-08-22T08:41:21.580

22 Hexagonal rooks 2012-07-30T19:59:48.720

22 Does this poset have a unique minimal element? 2012-12-24T16:35:44.933

22 A Question on 1, 2 ,3 Conjecture 2013-11-09T09:25:49.177

22 Non-linear expanders? 2014-05-28T14:17:01.173

21 Complete graph invariants? 2010-01-13T06:28:06.237

21 Red-blue alternating paths 2010-01-20T12:32:13.347

21 Graphs, K-theory and combinatorial balls: conjectures 2010-09-16T01:53:31.763

21 Obstructions for embedding a graph on a surface of genus g 2010-11-19T17:37:09.477

21 A graph with few edges everywhere 2010-12-18T13:27:34.507

21 Zero curves of Tutte Polynomials? 2015-10-30T03:35:50.750

20 "The" random tree 2009-11-18T19:21:48.587

20 What are some good examples of non-monotone graph properties? 2010-09-28T00:12:04.270

20 A strange sum over bipartite graphs 2012-03-05T07:00:48.230

20 Probability that random weights on $K_n$ satisfy triangle inequality 2012-06-17T00:47:31.723

20 Can one measure the infeasibility of four color proofs? 2013-09-15T21:35:32.750

20 Collection of conjectures and open problems in graph theory 2014-12-25T23:54:09.777

19 Why are Dynkin diagrams characterized by their eigenvalues? 2009-10-14T00:45:52.560

19 Local-Global approach to graph theory 2009-12-31T06:57:13.423

19 Why is edge-coloring less interesting than vertex-coloring? 2010-01-07T01:38:00.177

19 Gauss-Bonnet Theorem for Graphs? 2010-05-28T12:49:53.137

19 Are there Hamilton paths in Cayley graphs of Coxeter groups? 2012-03-20T16:35:20.763

19 Largest graphs of girth at least 6 2012-06-16T04:16:50.850

19 Monomer-Dimer tatami tilings need better relationships with other math. Summary of results 2012-07-26T07:11:38.960

19 A generalization of the triangle counting problem for simple weighted graphs 2012-08-10T14:44:49.740

19 Erdős, Harary, Tutte's "dimension of graph": Progress in last 48 yrs? 2013-08-30T01:01:23.550

19 A Ramsey avoidance game 2013-09-29T22:27:07.597

19 Is the Poset of Graphs Automorphism-free? 2013-12-31T04:23:03.630

19 What algebraic structures are related to the McGee graph? 2015-08-20T06:09:41.140

19 Which paths in a graph are orthogonal to all cycles? 2016-05-05T21:10:34.077

19 Girth of the symmetric group 2017-05-29T09:46:26.507

18 Finding a cycle of fixed length 2010-02-25T13:26:59.717

18 Which graphs are elementarily equivalent to their own disjoint sums? 2010-08-31T23:27:14.570

18 Drawing planar graphs with integer edge lengths 2011-02-02T15:57:29.133

18 Cops and drunken robbers 2011-03-11T05:21:51.157

18 Graphs with few induced subgraphs 2011-08-05T09:35:48.857

18 Is there an analogue of the Erdős–Gallai theorem for simplicial complexes? 2012-09-11T19:43:55.930

18 Determine or estimate the number of maximal triangle-free graphs on $n$ vertices 2014-03-06T08:25:15.370