Here are some papers available on-line (see here for journals and publication dates).

Published in 2004:

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

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

Published in 2005:

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).

Published in 2006:

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).

Published in 2007:

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.

Published in 2008:

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).

Published in 2009:

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).

Published in 2010:

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).

Published in 2011:

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

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

Published in 2012:

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).

Published in 2013:

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

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

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).

Published in 2014:

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

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

Extending the Gyarfas-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).

Published in 2015:

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

Criticality for multicommodity flows.

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

Not yet published:

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

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

Tournament minors (with Ilhee Kim).

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

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

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

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

Excluding paths and antipaths (with Maria Chudnovsky).

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

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

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

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

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

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

Colouring graphs with no odd holes (with Alex Scott).

Three steps towards Gyarfas' conjecture (with Maria Chudnovsky, Alex Scott).

Tree-chromatic number