Gelasio Salazar

Instituto de Fisica
Universidad Autonoma de San Luis Potosi
Av. Manuel Nava 6. Zona Universitaria
San Luis Potosi, SLP
Mexico 78290
Tel : +52 (444) 826 2362 to 65, Ext. 135
Fax : +52 (444) 813 3874
E-mail: gsalazar@ifisica.uaslp.mx

Research interests

I am mostly interested in Topological Graph Theory and in Discrete and Computational Geometry. Lately I have also developed an interest in Knot Theory.

Papers

Submitted

The knots that lie above all shadows (with Carolina Medina). Submitted (2019).
Convex drawings of the complete graph: topology meets geometry (with Alan Arroyo, Dan McQuillan, and Bruce Richter), submitted (2017).
Closing in on Hill's conjecture (with József Balogh and Bernard Lidický), submitted (2017).
Arrangements of pseudocircles on surfaces (with Carolina Medina and Edgardo Roldán-Pensado), submitted (2017).

Accepted

The unavoidable arrangements of pseudocircles (with Carolina Medina and Jorge Ramírez-Alfonsín). Proceedings of the American Mathematical Society. To appear (2019).
On the number of unknot diagrams (with Carolina Medina and Jorge Ramírez-Alfonsín). SIAM Journal in Discrete Mathematics. To appear (2019).
Toroidal Grid Minors and Stretch in Embedded Graphs (with Markus Chimani and Petr Hlineny). To appear in Journal of Combinatorial Theory Series B.

Published

Levi's Lemma, pseudolinear drawings of K_n, and empty triangles (with Alan Arroyo, Dan McQuillan, and Bruce Richter). J. Graph Theory 87, no. 4 (2018), 443-459.
On the pseudolinear crossing number (with Cesar Hernandez-Velez and Jesus Leanos). Journal of Graph Theory 84, no. 3 (2017), 297-310.
Drawings of K_n with the same rotation scheme are the same up to Reidemeister moves (Gioan's Theorem) (with A. Arroyo, D. McQuillan, and B. Richter). Australasian Journal of Combinatorics 67(2) (2017), 131-144. (Special issue in honour of Dan Archdeacon).
Large area convex holes in random point sets (with Octavio Arizmendi). SIAM J. Discrete Math. 30 (2016), no. 3, 1866-1875.
Characterizing 2-crossing-critical graphs (with Drago Bokal, Bogdan Oporowski, and Bruce Richter). Adv. in Appl. Math. 74 (2016), 23-208.
On the decay of crossing numbers of sparse graphs (with J. Balogh and J. Leaños). Journal of Graph Theory 80 (2015), 226-251.
On the hardness of the joint crossing number (with P. Hlineny). Lecture Notes in Computer Science 9472, Springer (2015), 603-613.
Book embeddings of regular graphs (with Jozsef Balogh). SIAM Journal in Discrete Mathematics 29 (2015), 811-822.
Embedding a graph-like continuum in some surface (with Robin Christian and Bruce Richter). Journal of Graph Theory 79 (2015), 159-165.
Shellable drawings and the cylindrical crossing number of K_n (with Bernardo Ábrego, Oswin Aichholzer, Silvia Fernández-Merchant, and Pedro Ramos). Discrete and Computational Geometry 52 (2014), 743-753.
Book drawings of complete bipartite graphs (with Etienne de Klerk and Dima Pasechnik). Discrete Applied Mathematics 167 (2014), 80-93.
The optimal drawings of K_5,n (with C. Hernández-Vélez and C. Medina). Electronic Journal of Combinatorics 21(4) (2014), #P4.1, 29 pp.
The 2-page crossing number of K_n (with B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, and P. Ramos). Discrete and Computational Geometry 49 (2013), 747-777.
Zarankiewicz's Conjecture is finite for each fixed m (with R. Christian and R.B. Richter). Journal of Combinatorial Theory Series B 103 (2013), 237-247.
Large convex holes in random point sets (with J. Balogh and H. González-Aguilar). Comp. Geom. 46 (2013), 725-733.
Crossing numbers (survey chapter) (with R.B. Richter). In: Handbook of Graph Theory, Second Edition. J.L. Gross, J. Yellen, and P. Zhang (Eds.). Chapman and Hall, 2013.
Making a graph crossing-critical by multiplying its edges (with L. Beaudou and C. Hernández-Vélez). Electronic Journal of Combinatorics 20 (1) (2013), Research paper 61, 14 pages.
Improved lower bounds on book crossing numbers of complete graphs (with D. V. Pasechnik and E. de Klerk). SIAM Journal on Discrete Mathematics, 27 (2012), 619-633.
The Erdős-Sós conjecture for geometric graphs (with L.F. Barba, R. Fabila, D. Lara, J. Leaños, C. Rodríguez, and F. Zaragoza). Disc. Math. and Theoretical Comp. Science 15 (2013), 93-100.
The rectilinear crossing number of K_n: closing in (or are we?) (with B. M. Ábrego and Silvia Fernández-Merchant). Thirty essays in Geometric Graph Theory (János Pach, Ed.). Springer (2013), pp. 5-18.
Convexifying monotone polygons while maintaining internal visibility (with O. Aichholzer, M. Cetina, R. Fabila, J.Leaños, and J. Urrutia). Lecture Notes in Computer Science 7579 (2012), 98-108.
The 2-page crossing number of K_n (with B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, and P. Ramos) In 28th Ann. ACM Symp. Computational Geometry, pp. 397-403, Chapel Hill, NC, USA, 2012.
Nested cycles in large triangulations and crossing-critical graphs (with C. Hernández-Velez and R. Thomas), Journal of Combinatorial Theory, 102 (2012), 86-92.
On k-edges, crossings, and halving lines of geometric drawings of K_n (with B. Abrego, M. Cetina, S. Fernández-Merchant, and J. Leaños), Discrete and Computational Geometry, 48 (2012), 192-215.
Visibility-preserving convexifications using single-vertex moves (with B. Abrego, M. Cetina, and J. Leaños), Information Processing Letters 112 (2012), 161-173.
Stars and bonds in crossing-critical graphs (with P. Hlineny), Journal of Graph Theory 65 (2010), 198-215.
The number of generalized balanced lines (with D. Orden and P. Ramos), Discrete and Computational Geometry 44 (2010), 805-811.
3-symmetric and 3-decomposable geometric drawings of K_n (with B. Abrego, M. Cetina, S. Fernández-Merchant, and J. Leaños), Discrete Applied Mathematics 158 (2010), 1240-1258.
The crossing number of a projective graph is quadratic in the face-width (with I. Gitler, P. Hlineny, and J. Leaños), Electronic Journal of Combinatorics 15 (2008), Research paper 46, 8 pp.
An extended lower bound on the number of k-edges to generalized configurations of points and the pseudolinear crossing number of K_n (with B. Ábrego, J. Balogh, S. Fernández--Merchant, and J. Leaños), Journal of Combinatorial Theory, Series A 115 (2008), 1257-1264.
A central approach to bound the number of crossings in a generalized configuration (with B. Abrego, S. Fernández-Merchant, and J. Leaños), Electronic Notes in Discrete Mathematics 30 (2008) 273-278.
The maximum number of halving lines and the rectilinear crossing number of K_n for n ≤ 27 (with B. Abrego, S. Fernández-Merchant, and J. Leaños), Electronic Notes in Discrete Mathematics 30 (2008) 261-266.
On the additivity of crossing numbers of graphs (with J. Leanos), Journal of Knot Theory and its Ramifications 17 (2008), 1043-1050.
A note on harmonic subgraphs in labelled geometric graphs (with G. Araujo, J. Balogh, R. Fabila, and J. Urrutia), Information Processing Letters 105 (2008), 98-102.
Simple Euclidean arrangements with no ( &ge 5) -gons are stretchable (with J. Leanos, C. Merino, and J. Urrutia), Discrete and Computational Geometry 38 (2007), 595-603.
On the crossing number of almost planar graphs (with P. Hlineny), Lecture Notes in Computer Science 4372 (2007), 162-173.
Large harmonious sets of non-crossing edges for n randomly labeled vertices in convex position (with Jozsef Balogh and Boris Pittel), Random Structures and Algorithms 30 (2007), 105-130.
The convex hull of every optimal pseudolinear drawing of K_n is a triangle (with J. Balogh, J. Leanos, S. Pan, and R.B. Richter), Australasian Journal of Combinatorics 38 (2007), 155-162.
Approximating the crossing number of toroidal graphs (with P. Hlineny). Lecture Notes in Computer Science 4835 , 148-159. Springer, 2007.
On k-sets, convex quadrilaterals, and the rectilinear crossing number of K_n (with Jozsef Balogh). Discrete and Computational Geometry 35 (2006), 671-690.
Improved bounds for the crossing numbers of K_m,n and K_n (with E. de Klerk, J. Maharry, D.V. Pasechnik, and R.B. Richter). SIAM Journal on Discrete Mathematics 20 (2006), 189-202.
Nearly-light cycles in embedded graphs and crossing-critical graphs , (with M. Lomeli), Journal of Graph Theory 53 (2006), 151-156.. In this paper, Theorem 6 is stated without proof. A referee for this paper asked that we write a proof of Theorem 6, and suggested that we posted it in this web page. The result is "Addendum to `Nearly-light cycles in embedded graphs and crossing-critical graphs'".
Two maps with large representativity on one surface (with B. Richter), Journal of Graph Theory 50 (2005), 234-245.
On the length of the longest alternating paths for multicoloured point sets in convex position (with C. Merino and J. Urrutia). Discrete Mathematics 360 (2006), 1791-1797.
Master-slave synchronization of affine cellular automaton pairs (with E. Ugalde and J. Urias), Discrete and Continuous Dynamical Systems 13 (2005), no. 2, 491--502.
On the Intersection number of matchings and minimum weight perfect matchings of multicolored point sets (with C. Merino and J. Urrutia). Graphs and Combinatorics 21 (2005), 333-341.
On the crossing numbers of loop networks and Generalized Petersen Graphs , Discrete Mathematics 302 (2005), no. 1-3, 243--253.
Spanning trees of multicoloured point sets with few intersections (with J. Leanos, C. Merino, and J. Urrutia), Lecture Notes in Computer Science 3330 , Springer-Verlag, Berlin, (2005), 113-122.
An improved bound for the crossing number of cr(C_m X C_n) : a self-contained proof using mostly combinatorial arguments (with E. Ugalde), Graphs and Combinatorics, 20 (2004), no. 2, 247--253.
Embedding grids in surfaces (with Jim Geelen and Bruce Richter), European Journal of Combinatorics 25 (2004), no. 6, 785--792.
The crossing number of C_m X C_n is as conjectured for n &ge m(m+1) (with Lev Glebsky), Journal of Graph Theory 47 (2004), no. 1, 53--72.
Morelia test: improving the efficiency of the Gabriel test and face routing in ad-hoc networks. Structural information and communication complexity (with P. Boone, E. Chavez, L. Glebsky, E. Kranakis, J. Opatrny, and J. Urrutia), Lecture Notes in Computer Science 3104, Springer-Verlag, Berlin, (2004), 23-34.
Small meshes of curves and their role in the analysis of optimal meshes , Discrete Mathematics 263 (2003), no. 1-3, 233-246.
Optimal meshes of curves in the Klein bottle (with Hector A. Juarez), Journal of Combinatorial Theory, Series B 88 (2003), no. 1, 185-188.
Infinite families of crossing-critical graphs with given average degree, Discrete Mathematics, 271 (2003), no. 1-3, 343-350.
The Crossing Number of P(N,3) (with Bruce Richter), Graphs and Combinatorics 18 (2002), no. 2, 381-394.
The Crossing Number of C₆ X C_n (with Bruce Richter), Australasian Journal of Combinatorics 23 (2001), 135-144.
Drawings of C_m X C_n with one disjoint family II , Journal of Combinatorial Theory, Series B, 82 (2001), no. 1, 161-165.
Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree (with E. Garcia-Moreno), Journal of Graph Theory 36 (2001), no. 3, 168-173.
A lower bound for the Crossing Number of C_m X C_n, Journal of Graph Theory 35 (2000), 222-226.
On a crossing number result of Richter and Thomassen, Journal of Combinatorial Theory, Series B, 79 (2000), no. 1, 98-99.
Drawings of C_m X C_n with one disjoint family, Journal of Combinatorial Theory Series B, 76 (1999), no. 2, 129-135.
On the Intersections of Systems of Curves, Journal of Combinatorial Theory Series B, 75 (1999), no. 1, 56-60.
On the Crossing Number of C_m X C_n , Journal of Graph Theory 28 (1998), no. 3, 163-170.
Internal symmetries of cellular automata via their polynomial representation (with J. Urias), Chaos 8 (1998), no. 3, 711-716.
Synchronization of cellular automaton pairs (with E. Ugalde and J. Urias), Chaos 8 (1998), no. 4, 814-818.
A cryptosystem based on cellular automata (with E. Ugalde and J. Urias), Chaos 8 (1998), no. 4, 819-822.
Random perturbations of iterated maps (with J. Urias), Journal of Mathematical Physics 37 (1996), no. 7, 3641-3643.
Traveling patterns in cellular automata (with A. Enciso, E. Ugalde and J. Urias), Chaos 6 (1996), no. 3, 493-503.

Students Supervision

Héctor Juárez (B.Sc., 1998)

Eduardo Calvillo (B.Sc., 1999)

Mario Lomelí (B.Sc., 2001)

Leticia Ramírez (B.Sc. Project, 2001)

Jetzabel Hernández (B.Sc., 2001)

Jesús Leaños (B.Sc. Project, 2002)

Adrián Cerda (B.Ss., 2003)

Héctor Juárez (M.Sc., 2000)

Alfonso Alba (M.Sc., 2001)

Mario Lomelí (M.Sc., 2003)

Jesús Leaños (M.Sc., 2003)

Mario Cetina (M.Sc., 2005)

Héctor Juárez (Ph.D., 2004)

Jesús Leaños (Ph.D., 2008)

Carolina Medina (M.Sc., 2012)

Enrique Arroyo (M.Sc., 2012)

Diana Navarro (M.Sc., 2013)

César Hernández-Vélez (Ph.D., 2013)

Sonia Rodríguez (M.Sc., 2015)

Rodrigo Dorantes (M.Sc., 2015)

Antonio Torres (M.Sc., in progress)

Carolina Medina (Ph.D., in progress)

Last modified: February 2017