When all directed cycles have length three

Thomassen’s theorem on the two-linkage problem in acyclic digraphs: a shorter proof

Distant digraph domination (with Tung Nguyen, Alex Scott).

Subdivisions and near-linear stable sets (with Tung Nguyen, Alex Scott).

Trees and near-linear stable sets (with Tung Nguyen, Alex Scott).

Clique covers in graphs with stability number two (with Sepehr Hajebi).

Excluding sums of Kuratowski graphs (with Neil Robertson).

Excluding disjoint Kuratowski graphs (with Neil Robertson).

Induced subgraph density. VII. The five-vertex path (with Tung Nguyen, Alex Scott).

Induced subgraph density. VI. Bounded VC-dimension (with Tung Nguyen, Alex Scott).

A counterexample to the coarse Menger conjecture (with Tung Nguyen, Alex Scott).

A shorter proof of the path-width theorem

Induced subgraph density. V. All paths approach Erdős-Hajnal (with Tung Nguyen, Alex Scott).

Induced subgraph density. IV. New graphs with the Erdős-Hajnal property (with Tung Nguyen, Alex Scott).

Induced subgraph density. II. Sparse and dense sets in cographs (with Jacob Fox, Tung Nguyen, Alex Scott).

Some results and problems on tournament structure (with Tung Nguyen, Alex Scott).

Induced subgraph density. III. Cycles and subdivisions (with Tung Nguyen, Alex Scott).

Dense minors of graphs with independence number two (with Sergey Norin).

Small families under subdivision (with Maria Chudnovsky and Martin Loebl).

Cut coloring and circuit covering (with Matt Devos, Thor Johnson).

A bound on the excluded minors for a surface

Pure pairs. VIII. Excluding a sparse graph (with Alex Scott and Sophie Spirkl).

Graphs with all holes the same length (with Linda Cook, Jake Horsfield, Myriam Preissmann, Cléopheé Robin, Ni Luh Dewi Sintiari, Nicolas Trotignon, Kristina Vušković).

Pure pairs. IX. Transversal trees (with Alex Scott, Sophie Spirkl).

Clique covers of H-free graphs (with Tung Nguyen, Alex Scott, Stephan Thomassé).

Induced subgraph density. I. A loglog step towards Erdős-Hajnal (with Matija Bucić, Tung Nguyen, Alex Scott).

Cops and robbers on P ₅-free graphs (with Maria Chudnovsky, Sergey Norin, Jérémie Turcotte).

Polynomial bounds for chromatic number. VIII. Excluding a path and a complete multipartite graph (with Tung Nguyen, Alex Scott).

A note on the Gyárfás-Sumner conjecture (with Tung Nguyen, Alex Scott).

On a problem of El-Zahar and Erdős (with Tung Nguyen, Alex Scott).

Bounded-diameter tree-decompositions (with Eli Berger).

Pure pairs. X. Tournaments and the strong Erdős-Hajnal property (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Bipartite graphs with no K₆ minor (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Polynomial bounds for chromatic number. V. Excluding a tree of radius two and a complete multipartite graph (with Alex Scott).

Induced paths in graphs without anticomplete cycles (with Tung Nguyen, Alex Scott).

Polynomial bounds for chromatic number. VI. Adding a four-vertex path (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Strengthening Rodl's theorem (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Polynomial bounds for chromatic number. VII. Disjoint holes (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Pure pairs. VII. Homogeneous submatrices in 0/1-matrices with a forbidden submatrix (with Alex Scott and Sophie Spirkl).

Erdős-Hajnal for graphs with no five-hole (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Pure pairs. V. Excluding some long subdivision (with Alex Scott and Sophie Spirkl).

Even-hole-free graphs still have bisimplicial vertices (with Maria Chudnovsky).

Pure pairs. IV. Trees in bipartite graphs (with Alex Scott and Sophie Spirkl).

Polynomial bounds for chromatic number. IV. A near-polynomial bound for excluding the five-vertex path (with Alex Scott, Sophie Spirkl).

Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree (with Alex Scott, Sophie Spirkl).

Proof of a conjecture of Plummer and Zha (with Maria Chudnovsky).

Detecting a long even hole (with Linda Cook).

Concatenating bipartite graphs (with Maria Chudnovsky, Patrick Hompe, Alex Scott and Sophie Spirkl).

Polynomial bounds for chromatic number. III. Excluding a double star (with Alex Scott, Sophie Spirkl).

Polynomial bounds for chromatic number. II. Excluding a star-forest (with Alex Scott, Sophie Spirkl).

Pure pairs. VI. Excluding an ordered tree (with Alex Scott and Sophie Spirkl).

Induced subgraphs of bounded treewidth and the container method (with Tara Abrishami, Maria Chudnovsky, Marcin Pilipczuk, Paweł Rzążewski).

A note on simplicial cliques (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Pure pairs. II. Excluding all subdivisions of a graph (with Maria Chudnovsky, Alex Scott and Sophie Spirkl).

Subdivided claws and the clique-stable set separation property (with Maria Chudnovsky).

Finding a shortest odd hole (with Maria Chudnovsky, Alex Scott).

Finding an induced path that is not a shortest path (with Eli Berger, Sophie Spirkl).

Erdős-Hajnal for cap-free graphs (with Maria Chudnovsky).

Induced subgraphs of graphs with large chromatic number. V. Chandeliers and strings (with Maria Chudnovsky, Alex Scott).

Detecting a long odd hole (with Maria Chudnovsky and Alex Scott).

Pure pairs. I. Trees and linear anticomplete pairs (with Maria Chudnovsky, Alex Scott and Sophie Spirkl).

A survey of chi-boundedness (with Alex Scott).

Pure pairs. III. Sparse graphs with no polynomial-sized anticomplete pairs (with Maria Chudnovsky, Jacob Fox, Alex Scott and Sophie Spirkl).

Proof of the Kalai-Meshulam conjecture (with Maria Chudnovsky, Alex Scott and Sophie Spirkl).

Short directed cycles in bipartite digraphs (with Sophie Spirkl).

Induced subgraphs of graphs with large chromatic number. VI. Banana trees (with Alex Scott)

Corrigendum to ``Bisimplicial vertices in even-hole-free graphs'' (with Louigi Addario-Berry, Maria Chudnovsky, Frederic Havet, Bruce Reed).

Induced subgraphs of graphs with large chromatic number. VII. Gyárfás' complementation conjecture (with Alex Scott).

Detecting an odd hole (with Maria Chudnovsky, Alex Scott and Sophie Spirkl).

Excluding the fork and antifork (with Maria Chudnovsky and Linda Cook).

Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes (with Maria Chudnovsky, Alex Scott, Sophie Spirkl).

Clustered colouring in minor-closed classes (with Sergey Norin, Alex Scott and David Wood).

Induced subgraphs of graphs with large chromatic number. X. Holes with specific residue (with Alex Scott).

Large rainbow matchings in general graphs (with Ron Aharoni, Eli Berger, Maria Chudnovsky, David Howard).

Girth six cubic graphs have Petersen minors (with Neil Robertson, Robin Thomas).

Towards Erdős-Hajnal for graphs with no 5-hole (with Maria Chudnovsky, Jacob Fox, Alex Scott and Sophie Spirkl).

H-colouring P t -free graphs in subexponential time (with Carla Groenland, Karolina Okrasa, Paweł Rzążewski, Alex Scott, and Sophie Spirkl).

Induced subgraphs of graphs with large chromatic number. XIII. New brooms (with Alex Scott).

Excluded minors in cubic graphs (with Neil Robertson, Robin Thomas).

Near-domination in graphs (with Bruce Reed, Alex Scott).

Caterpillars in Erdős-Hajnal (with Anita Liebenau, Marcin Pilipczuk and Sophie Spirkl).

Induced subgraphs of graphs with large chromatic number. XII. Distant stars (with Maria Chudnovsky, Alex Scott).

Disjoint paths in unions of tournaments (with Maria Chudnovsky, Alex Scott).

Bad news for chordal partitions (with Alex Scott and David Wood).

Induced subgraphs of graphs with large chromatic number. XI. Orientations (with Maria Chudnovsky, Alex Scott).

Triangle-free graphs with no six-vertex induced path (with Maria Chudnovsky, Sophie Spirkl, Mingxian Zhong).

Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes (with Alex Scott).

Domination in tournaments (with Maria Chudnovsky, Ringi Kim, Chun-Hung Liu, Stephan Thomassé).

Even pairs and prisms corners in Berge graphs (with Maria Chudnovsky, Frederic Maffray, Sophie Spirkl).

Induced subgraphs of graphs with large chromatic number. III. Long holes (with Maria Chudnovsky, Alex Scott).

Induced subgraphs of graphs with large chromatic number. IX. Rainbow paths (with Alex Scott).

Rooted grid minors (with Daniel Marx, Paul Wollan).

Colouring perfect graphs with bounded clique number (with Maria Chudnovsky, Aurelie Lagoutte, Sophie Spirkl).

Cyclically five-connected cubic graphs (with Neil Robertson, Robin Thomas).

Majority colourings of digraphs (with Stephan Kreutzer, Sang-il Oum, Dominic van der Zypen, David Wood).

Immersion in four-edge-connected graphs (with Maria Chudnovsky, Zdenek Dvorak, Tereza Klimosova).

Bipartite minors (with Maria Chudnovsky, Gil Kalai, Eran Nevo, Isabella Novik).

Tree-chromatic number

Three-edge-colouring doublecross cubic graphs (with Katherine Edwards, Daniel Sanders, Robin Thomas).

Unavoidable induced subgraphs in large graphs with no homogeneous sets (with Maria Chudnovsky, Ringi Kim, Sang-Il Oum).

Induced subgraphs of graphs with large chromatic number. II. Three steps towards Gyárfás' conjectures (with Maria Chudnovsky, Alex Scott).

Disjoint dijoins (with Maria Chudnovsky, Katherine Edwards, Ringi Kim, Alex Scott).

Hadwiger's conjecture.

Induced subgraphs of graphs with large chromatic number. I. Odd holes (with Alex Scott).

Disjoint paths in tournaments (with Maria Chudnovsky, Alex Scott).

Edge-disjoint paths in digraphs with bounded independence number (with Alexandra Fradkin).

Criticality for multicommodity flows.

Tree-width and planar minors (with Alexander Leaf).

Tournament minors (with Ilhee Kim).

Excluding a substar and an antisubstar (with Maria Chudnovsky, Sergey Norin, Bruce Reed).

Wheel-free planar graphs (with Pierre Aboulker, Maria Chudnovsky, Nicolas Trotignon).

Edge-colouring eight-regular planar graphs (with Maria Chudnovsky, Katherine Edwards).

Edge-colouring seven-regular planar graphs (with Maria Chudnovsky, Katherine Edwards, Ken-ichi Kawarabayashi).

Excluding paths and antipaths (with Maria Chudnovsky).

A relative of Hadwiger's conjecture (with Katherine Edwards, Dong Yeap Kang, Jaehoon Kim, Sang-Il Oum).

Proof of a conjecture of Bowlin and Brin on four-colouring triangulations.

Rao's degree sequence conjecture (with Maria Chudnovsky).

Extending the Gyárfás-Sumner conjecture (with Maria Chudnovsky).

Excluding pairs of graphs (with Maria Chudnovsky, Alex Scott).

Tournaments with near-linear transitive subsets (with Krzysztof Choromanski, Maria Chudnovsky).

Tournaments and colouring (with E. Berger, K. Choromanski, M. Chudnovsky, J. Fox, M. Loebl, A. Scott, S. Thomassé).

A counterexample to a conjecture of Schwartz (with F. Brandt, M. Chudnovsky, I. Kim, G. Liu, S. Norin, A. Scott, S. Thomassé).

Tournament path-width and topological containment (with Alexandra Fradkin).

A local strengthening of Reed's omega, Delta, and chi conjecture for quasi-line graphs (with M. Chudnovsky, A. King, M. Plumettaz).

Detecting an induced net subdivision (with Maria Chudnovsky, Nicolas Trotignon).

Graph minors. XXII. Irrelevant vertices in linkage problems (with Neil Robertson).

Claw-free graphs VII. Quasi-line graphs (with Maria Chudnovsky).

Perfect matchings in planar cubic graphs (with Maria Chudnovsky).

Packing seagulls (with Maria Chudnovsky).

Finding minimum clique capacity (with Maria Chudnovsky and Sang-Il Oum).

Tournament immersion and cutwidth (with Maria Chudnovsky and Alexandra Fradkin).

Growing without cloning (with Maria Chudnovsky).

Three-colourable perfect graphs without even pairs (with Maria Chudnovsky).

The edge-density for K_{2,t} minors (with Maria Chudnovsky and Bruce Reed).

A well-quasi-order for tournaments (with Maria Chudnovsky).

Graph minors. XXIII. Nash-Williams' immersion conjecture (with Neil Robertson).

Claw-free graphs VI. Colouring (with Maria Chudnovsky).

The three-in-a-tree problem (with Maria Chudnovsky).

K_4-free graphs with no odd holes (with Maria Chudnovsky, Neil Robertson and Robin Thomas).

Counting paths in digraphs (with Blair Sullivan).

Graph minors. XXI. Graphs with unique linkages (with Neil Robertson).

On the odd-minor variant of Hadwiger's conjecture (with Jim Geelen, Bert Gerards, Bruce Reed, Adrian Vetta).

Even pairs in Berge graphs (with Maria Chudnovsky).

Claw-free graphs II. Non-orientable prismatic graphs (with Maria Chudnovsky).

Claw-free graphs III. Circular interval graphs (with Maria Chudnovsky).

Claw-free graphs IV. Decomposition theorem (with Maria Chudnovsky).

Claw-free graphs V. Global structure (with Maria Chudnovsky).

Cycles in dense digraphs (with Maria Chudnovsky, Blair Sullivan).

Solution of three problems of Cornuejols (with Maria Chudnovsky).

Bisimplicial vertices in even-hole-free graphs (with L.Addario-Berry, M.Chudnovsky, F.Havet, B.Reed).

The roots of the independence polynomial of a claw-free graph (with Maria Chudnovsky).

Claw-free graphs I. Orientable prismatic graphs (with Maria Chudnovsky).

Excluding induced subgraphs (with Maria Chudnovsky).

Testing branchwidth (with Sang-Il Oum). See also a Corrigendum.

The strong perfect graph theorem (with M. Chudnovsky, N. Robertson, R. Thomas).

How the proof of the strong perfect graph conjecture was found.

Approximating clique-width and branch-width (with Sang-Il Oum).

Proper minor-closed families are small (with Serguei Norine, Robin Thomas and Paul Wollan).

Certifying large branch-width (with Sang-Il Oum).

Packing non-zero A-paths in group-labeled graphs (with M. Chudnovsky, J. Geelen, A. Gerards, L. Goddyn, M. Lohman).

Recognizing Berge graphs (with M. Chudnovsky, G. Cornuejols, X. Liu, K. Vuskovic).

Detecting even holes (with Maria Chudnovsky and Ken-ichi Kawarabayashi).

The structure of claw-free graphs (with Maria Chudnovsky).

Graph minors. XX. Wagner's conjecture (with Neil Robertson).

Hadwiger's conjecture for line graphs (with Bruce Reed).

Excluding any graph as a minor allows a low tree-width 2-coloring (with M. Devos, G. Ding, B. Oporowski, B. Reed, D. Sanders and D. Vertigan).

Graph minors. XIX. Well-quasi-ordering on a surface (with Neil Robertson).

Tour merging via branch-decomposition (with Bill Cook).

Progress on perfect graphs (with M. Chudnovsky, N. Robertson and R. Thomas).

Graph minors. XVIII. Tree-decompositions and well-quasi-ordering (with Neil Robertson).

Graph minors. XVI. Excluding a non-planar graph (with Neil Robertson).

Extending partial 3-colourings in a planar graph (with Matt Devos).

Colouring eulerian triangulations (with J. Hutchinson and B. Richter).

Colouring locally bipartite graphs on surfaces (with Bojan Mohar).

Directed tree-width (with T. Johnson, N. Robertson and R. Thomas).

Node placement and sizing for copper broadband access networks (with T. Carpenter, M. Eiger and D. Shallcross).

Spanning trees with many leaves (with G. Ding and T. Johnson).

Long cycles in critical graphs (with N. Alon and M. Krivelevich).

Permanents, Pfaffian orientations, and even directed circuits (with N. Robertson and R. Thomas).

Graph minors. XVII. Taming a vortex (with Neil Robertson).

Call routing and the ratcatcher (with R. Thomas).

Graph minors. X. Obstructions to tree-decomposition (with Neil Robertson).

Graph minors. IV. Tree-width and well-quasi-ordering (with Neil Robertson).

Graph minors. A survey (with Neil Robertson).