**Matching Theory and Pfaffian Orientations:
**

- A new proof of a characterisation of Pfaffian bipartite graphs
(with C. H. C. Little and Kee L. Teo),
*J. Comb. Theory B***91**(2004), 123-126. - Unions of perfect matchings in cubic graphs (with T. Kaiser and D. Kral'), in "Topics in Discrete Mathematics" (M. Klazar, J. Kratochvil, J. Matousek, R. Thomas, P. Valtr, eds.), Springer (2006), 225-230.
- Minimal bricks (with R. Thomas), J. Comb. Theory B 96 (2006), 505-513.
- Generating bricks (with R. Thomas), J. Comb. Theory B 97 (2007), 769-817.
- Pfaffian graphs, T-joins
and crossing numbers, Combinatorica 28 (2008), 89-98.

(Conference version: Drawing Pfaffian graphs,*Graph Drawing, 12th International Symposium, Lecture Notes in Computer Science*, 3383 (2005), 371-376.) - Pfaffian labelings and signs of edge-colorings (with R. Thomas), Combinatorica 28 (2008), 99-111.
- Minimally non-Pfaffian graphs (with R. Thomas), J. Comb. Theory B 98 (2008), 1038-1055.
- Drawing 4-Pfaffian graphs on the torus, Combinatorica 29 (2009), 109-119.
- Exponentially many perfect matchings in cubic graphs (with L. Esperet, F. Kardos, A. King and D. Kral'), Adv. Math. 227 (2011), 1646-1664.
- Holographic algorithms
without matchgates (with J. M. Lansberg and J. Morton),
*Linear Algebra Appl.*,**438**(2013), 782--795.

- Proper minor-closed families are small (with P. Seymour, R. Thomas and P. Wollan), J. Comb. Theory B 96 (2006), 754-757.
- Small graph classes and
bounded expansion (with Z. Dvorak), J. Comb. Theory B
**100**(2010), 171-175.

- New tools and results in graph minor structure theory,
*Surveys in Combinatorics***424**(2015), 221-260.

- Strongly sublinear separators and polynomial expansion (with Z.
Dvorak),
*SIAM J. Discrete Math.***30(2)**(2016), 1095–1101.

- Non-planar extensions of subdivisions of planar graphs (with R.
Thomas), J. Comb. Theory B
**121**(2016), 326-366.

- The extremal function for disconnected minors (with E. Csóka, I. Lo, H. Wu and L. Yepremyan), J. Comb. Theory B
**126**(2017), 162-174.

- K
_{6}minors in 6-connected graphs of bounded tree-width (with K. Kawarabayashi, R. Thomas and P. Wollan), submitted.

- K
_{6}minors in large 6-connected graphs (with K. Kawarabayashi, R. Thomas and P. Wollan), submitted.

- Treewidth of graphs with balanced separations (with Z.
Dvorak), submitted.

- Treewidth of grid subsets (with E.
Berger and Z. Dvorak), submitted.

- Orthogonal Tree Decompositions of Graphs (with V. Dujmovic, G. Joret, P. Morin and D. Wood), submitted.

- Clustered Colouring in Minor-Closed Classes (with A. Scott, P. Seymour and D. Wood), submitted.

- Islands in minor-closed classes. I. Bounded treewidth and separators (with Z.
Dvorak)

Extremal Combinatorics:

- Undecidability of linear inequalities in graph homomorphism densities (with H. Hatami), J. Amer. Math. Soc., 24 (2011), 547-565.
- Turan graphs and the number of colorings, SIAM J. Discrete Math., 25 (2011), 260-266.
- Non-three-colorable common graphs exist (with H. Hatami, J. Hladky, D. Kral' and A.
Razborov),
*Combin. Probab. Comput.*,**21**(2012), 734--742. - On the number of pentagons in
triangle-free graphs (with H. Hatami, J. Hladky, D. Kral' and A. Razborov),
*J. Combin. Theory Ser. A*,**120**(2013), 722-732. - The inducibility of blow-up graphs (with H. Hatami and J. Hirst),
*J. Combin. Theory Ser. B*,**109**(2014), 196-212. - Sparse halves in dense triangle-free graphs (with L. Yepremyan),
*J. Combin. Theory Ser. B*,**115**(2015), 1-25. - Erdős-Szekeres without induction (with Y. Yuditsky),
*Disc. and Comp. Geometry***55**(2016), 963-971. - Turán number of generalized triangles (with L. Yepremyan),
*J. Combin. Theory Ser. A*,**146**(2017), 312-343. - Counting flags in triangle-free digraphs (with J. Hladky and D. Kral'),
*Combinatorica*,**37**(2017), 49-76. - Turán numbers of extensions (with L. Yepremyan), submitted.
- Triangle-independent sets vs. cuts (with Y. R. Sun), submitted.
- Asymptotics of Ramsey numbers of double stars. (with Y. R. Sun and Y. Zhao), submitted.
- On the boundary of the region defined by homomorphism densities (with H. Hatami)
- A Turán theorem for extensions via an Erdős-Ko-Rado theorem for Lagrangians (with A. Bene Watts and L. Yepremyan)

- The circular chromatic
index of flower snarks (with M. Ghebleh, D. Kral' and R.
Thomas), Electronic Journal
of Combinatorics,
**13(1)**(2006), #N20, 7pp. - On two questions
about circular choosability,
*J. Graph Theory*58 (2008), 261-269. - Circular degree
choosability (with X. Zhu), Electronic Journal
of Combinatorics,
**15(1)**(2008), #R100, 8pp. - Graphs with full rank 3-color matrix and few 3-colorings (with J.-S. Sereni), J. Comb. Theory B 98 (2008), 1115-1116.
- Circular
choosability via combinatorial Nullstellensatz (with
T.-L. Wong and X. Zhu),
*J. Graph Theory*59 (2008), 190-204. - Circular consecutive
choosability of
*k*-choosable graphs (with D. Liu, Z. Pan and X. Zhu), J. Graph Theory 67 (2011), 178-197.

- List coloring with requests (with Z. Dvorak and L. Postle), submitted.

Analogies Between Graphs and Riemann Surfaces:

- Riemann-Roch and
Abel-Jacobi theory on a finite graph (with M. Baker), Adv. Math. 215(2) (2007), 766-788.

- Harmonic morphisms and hyperelliptic graphs (with M. Baker), Int. Math. Res. Notices (2009), 42 pp.
- Jacobians of near-complete
and threshold graphs (with P. Whalen), European J. Combin.
**32**(2011), 1368--1376.

- Rank of divisors on
tropical curves (with J. Hladky and D. Kral'),
*J. Combin. Theory Ser. A*,**120**(2013), 1521-1538.

Game theory:

- Set intersections, perfect graphs, and voting in agreeable
societies (with D. E. Berg, F. E. Su, R. Thomas and P.
Wollan),
*Am. Math. Mon.***117**(2010), 27-39. - A
counterexample to a conjecture of Schwartz (with F.
Brandt, M. Chudnovsky, I. Kim, G. Liu, A. Scott, P. Seymour
and S. Thomasse),
*Soc. Choice Welf.*,**40(3)**(2013), 739-743. - Polylogarithmic Supports are required for Approximate Well-Supported Nash Equilibria below 2/3 (with Y. Anbalagan, R. Savani and A. Vetta),
*Web and Internet Economics, LNCS*,**8289**(2013), 15--23. - A Near-Optimal Mechanism for Impartial Selection (with N. Bousquet and A. Vetta),
*Web and Internet Economics, LNCS*,**8877**(2014), 133-146. - Large Supports are required for Well-Supported Nash Equilibria (with Y. Anbalagan, H. Huang, S. Lovett, A. Vetta and H. Wu),
*LIPIcs. APPROX/RANDOM 15***40**(2015), 78-84.

Other
Topics:

- A polynomial lower bound for the size of a k-min-wise
independent set of permutations
**,***J. Math. Sci. (N. Y.)***118**(2003), no. 2, 4994-5000. - Markov bases of binary
graph models of K
_{4}-minor free graphs (with D. Kral' and O. Pangrac), J. Comb. Theory A 117 (2010), 759-765. - The entropy of random-free graphons and properties (with H. Hatami),
*Combin. Probab. Comput.*,**22**, (2013) 517-526. - Excluding a substar and an anti-substar (with M. Chudnovsky, B. Reed and P. Seymour),
*SIAM J. Discrete Math.*,**29(1)**(2015), 297–308. - Flag algebras and the stable coefficients of the Jones polynomial (with S. Garoufalidis and T. Vuong),
*European J. Combin.*,**51**(2016), 165-189. - A distribution on triples with maximum entropy marginal
- Virtually fibering right-angled Coxeter groups (with K. Jankiewicz and D. Wise), submitted.
- Distribution of coefficients of rank polynomials for random sparse graphs, (with. D. Jakobson and L. Turner),
*submitted*. - Connectivity of addable classes of forests,
*manuscript*.