selected publications
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article
- Convex drawings of the complete graph: topology meets geometry. Ars Mathematica Contemporanea. 22:-. 2022-01-01
- Drawings of complete graphs in the projective plane. Journal of Graph Theory. 97:426-440. 2021-01-01
- Embeddability of Arrangements of Pseudocircles and Graphs on Surfaces. Discrete and Computational Geometry. 64:386-395. 2020-01-01
- Toroidal grid minors and stretch in embedded graphs. Journal of Combinatorial Theory. Series B. 140:323-371. 2020-01-01
- Closing in on Hill's conjecture. SIAM Journal on Discrete Mathematics. 33:1261-1276. 2019-01-01
- On the number of unknot diagrams. SIAM Journal on Discrete Mathematics. 33:306-326. 2019-01-01
- The knots that lie above all shadows. Topology and its Applications. 268:-. 2019-01-01
- The unavoidable arrangements of pseudocircles. Proceedings of the American Mathematical Society. 147:3165-3175. 2019-01-01
- When can a link be obtained from another using crossing exchanges and smoothings?. Topology and its Applications. 260:13-22. 2019-01-01
- Levi's Lemma, pseudolinear drawings of Kn, and empty triangles. Journal of Graph Theory. 87:443-459. 2018-01-01
- Drawings of Kn with the same rotation scheme are the same up to triangle-flips (Gioan’s Theorem). Australasian Journal of Combinatorics. 67:131-144. 2017-01-01
- On the Pseudolinear Crossing Number. Journal of Graph Theory. 84:297-310. 2017-01-01
- Characterizing 2-crossing-critical graphs. Advances in Applied Mathematics. 74:23-208. 2016-01-01
- Large area convex holes in random point sets. SIAM Journal on Discrete Mathematics. 30:1866-1875. 2016-01-01
- Book embeddings of regular graphs. SIAM Journal on Discrete Mathematics. 29:811-822. 2015-01-01
- Embedding a graph-like continuum in some surface. Journal of Graph Theory. 79:159-165. 2015-01-01
- On the Decay of Crossing Numbers of Sparse Graphs. Journal of Graph Theory. 80:226-251. 2015-01-01
- Book drawings of complete bipartite graphs. Discrete Applied Mathematics. 167:80-93. 2014-01-01
- Shellable Drawings and the Cylindrical Crossing Number of Kn. Discrete and Computational Geometry. 52:743-753. 2014-01-01
- The optimal drawings of K5,n. Electronic Journal of Combinatorics. 21:-. 2014-01-01
- Improved lower bounds on book crossing numbers of complete graphs. SIAM Journal on Discrete Mathematics. 27:619-633. 2013-01-01
- Large convex holes in random point sets. Computational Geometry: Theory and Applications. 46:725-733. 2013-01-01
- Making a graph crossing-critical by multiplying its edges. Electronic Journal of Combinatorics. 20:-. 2013-01-01
- More on the crossing number of Kn: Monotone drawings. Electronic Notes in Discrete Mathematics. 44:411-414. 2013-01-01
- The 2-Page Crossing Number of Kn. Discrete and Computational Geometry. 49:747-777. 2013-01-01
- The Erdos-Sós conjecture for geometric graphs. Discrete Mathematics and Theoretical Computer Science. 15:93-100. 2013-01-01
- Zarankiewicz's Conjecture is finite for each fixed m. Journal of Combinatorial Theory. Series B. 103:237-247. 2013-01-01
- Nested cycles in large triangulations and crossing-critical graphs. Journal of Combinatorial Theory. Series B. 102:86-92. 2012-01-01
- On ≤ k-Edges, Crossings, and Halving Lines of Geometric Drawings of K n. Discrete and Computational Geometry. 48:192-215. 2012-01-01
- Visibility-preserving convexifications using single-vertex moves. Information Processing Letters. 112:161-163. 2012-01-01
- Asymptotically settling Zarankiewicz's Conjecture in finite time, for each m. Electronic Notes in Discrete Mathematics. 38:279-284. 2011-01-01
- There is a unique crossing-minimal rectilinear drawing of K18. Electronic Notes in Discrete Mathematics. 38:547-552. 2011-01-01
- 3-symmetric and 3-decomposable geometric drawings of Kn. Discrete Applied Mathematics. 158:1240-1258. 2010-01-01
- Stars and bonds in crossing-critical graphs. Journal of Graph Theory. 65:198-215. 2010-01-01
- The Number of Generalized Balanced Lines. Discrete and Computational Geometry. 44:805-811. 2010-01-01
- A central approach to bound the number of crossings in a generalized configuration. Electronic Notes in Discrete Mathematics. 30:273-278. 2008-01-01
- A note on harmonic subgraphs in labelled geometric graphs. Information Processing Letters. 105:98-102. 2008-01-01
- An extended lower bound on the number of (≤ k)-edges to generalized configurations of points and the pseudolinear crossing number of Kn. Journal of Combinatorial Theory. Series A. 115:1257-1264. 2008-01-01
- On the additivity of crossing numbers of graphs. Journal of Knot Theory and its Ramifications. 17:1043-1050. 2008-01-01
- Stars and Bonds in Crossing-Critical Graphs. Electronic Notes in Discrete Mathematics. 31:271-275. 2008-01-01
- The crossing number of a projective graph is quadratic in the face - Width. Electronic Journal of Combinatorics. 15:-. 2008-01-01
- The maximum number of halving lines and the rectilinear crossing number of Kn for n ≤ 27. Electronic Notes in Discrete Mathematics. 30:261-266. 2008-01-01
- Simple Euclidean arrangements with no (≥ 5)-gons. Discrete and Computational Geometry. 38:595-603. 2007-01-01
- The convex hull of every optimal pseudolinear drawing of kn is a triangle. Australasian Journal of Combinatorics. 38:155-162. 2007-01-01
- The crossing number of a projective graph is quadratic in the face-width. Electronic Notes in Discrete Mathematics. 29:219-223. 2007-01-01
- Improved bounds for the crossing numbers of Km,n and K n. SIAM Journal on Discrete Mathematics. 20:189-202. 2006-01-01
- Nearly light cycles in embedded graphs and crossing-critical graphs. Journal of Graph Theory. 53:151-156. 2006-01-01
- On the length of longest alternating paths for multicoloured point sets in convex position. Discrete Mathematics. 306:1791-1797. 2006-01-01
- k-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn*. Discrete and Computational Geometry. 35:671-690. 2006-01-01
- Master-slave synchronization of affine cellular automaton pairs. Discrete and Continuous Dynamical Systems. 13:491-502. 2005-01-01
- On the intersection number of matchings and minimum weight perfect matchings of multicolored point sets. Graphs and Combinatorics. 21:333-341. 2005-01-01
- Two maps with large representativity on one surface. Journal of Graph Theory. 50:234-245. 2005-01-01
- An improved bound for the crossing number of Cm×C n: A self-contained proof using mostly combinatorial arguments. Graphs and Combinatorics. 20:247-253. 2004-01-01
- Embedding grids in surfaces. European Journal of Combinatorics. 25:785-792. 2004-01-01
- Morelia test: Improving the efficiency of the Gabriel test and face routing in ad-hoc networks. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 3104:23-34. 2004-01-01
- The crossing number of Cm × Cn is as conjectured for n ≥ m(m%2b1). Journal of Graph Theory. 47:53-72. 2004-01-01
- Infinite families of crossing-critical graphs with given average degree. Discrete Mathematics. 271:343-350. 2003-01-01
- Optimal meshes of curves in the Klein bottle. Journal of Combinatorial Theory. Series B. 88:185-188. 2003-01-01
- Small meshes of curves and their role in the analysis of optimal meshes. Discrete Mathematics. 263:233-246. 2003-01-01
- The crossing number of P(N, 3). Graphs and Combinatorics. 18:381-394. 2002-01-01
- Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree. Journal of Graph Theory. 36:168-173. 2001-01-01
- The crossing number of C6 × Cn. Australasian Journal of Combinatorics. 23:135-143. 2001-01-01
- A lower bound for the crossing number of Cm × Cn. Journal of Graph Theory. 35:222-226. 2000-01-01
- On a Crossing Number Result of Richter and Thomassen. Journal of Combinatorial Theory. Series B. 79:98-99. 2000-01-01
- Drawings of Cm×Cn with One Disjoint Family. Journal of Combinatorial Theory. Series B. 76:129-135. 1999-01-01
- On the Intersections of Systems of Curves. Journal of Combinatorial Theory. Series B. 75:56-60. 1999-01-01
- A cryptosystem based on cellular automata. Chaos. 8:819-822. 1998-01-01
- Internal symmetries of cellular automata via their polynomial representation. Chaos. 8:711-716. 1998-01-01
- On the Crossing Number of Cm x Cn. Journal of Graph Theory. 28:163-170. 1998-01-01
- Synchronization of cellular automaton pairs. Chaos. 8:814-818. 1998-01-01
- Random perturbations of iterated maps. Journal of Mathematical Physics. 37:3641-3643. 1996-01-01
- Traveling patterns in cellular automata. Chaos. 6:493-503. 1996-01-01
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chapter
- The rectilinear crossing number of K n : Closing in (or are we?). Thirty Essays on Geometric Graph Theory. 5-18. 2013-01-01
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conference paper
- On hardness of the joint crossing number. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 603-613. 2015-01-01
- Convexifying monotone polygons while maintaining internal visibility. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 98-108. 2012-01-01
- The 2-page crossing number of K n. Proceedings of the Annual Symposium on Computational Geometry. 397-403. 2012-01-01
- Approximating the crossing number of toroidal graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 148-159. 2007-01-01
- Large harmonic sets of noncrossing edges for n randomly labeled vertices in convex position. Random Structures and Algorithms. 105-130. 2007-01-01
- On the crossing number of almost planar graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 162-173. 2007-01-01
- On the crossing numbers of loop networks and generalized Petersen graphs. Discrete Mathematics. 243-253. 2005-01-01
- Spanning trees of multicoloured point sets with few intersections. Lecture Notes in Computer Science. 113-122. 2005-01-01
- Improved bounds for the number of (≤ k)-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn. Lecture Notes in Computer Science. 25-35. 2004-01-01
- Noisy attractors of Markov maps. IEEE International Symposium on Information Theory - Proceedings. 422-. 1995-01-01