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
Email: 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
Published

Levi's Lemma, pseudolinear drawings of K_{n}, and
empty
triangles (with Alan Arroyo, Dan McQuillan, and Bruce Richter). Journal of
Graph Theory (to appear, 2018).

On the pseudolinear crossing number
(with Cesar HernandezVelez and Jesus Leanos). Journal of Graph Theory
84, no. 3 (2017), 297310.

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), 131144. (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,
18661875.

Characterizing 2crossingcritical graphs
(with Drago Bokal, Bogdan Oporowski, and Bruce Richter).
Adv. in Appl. Math. 74 (2016), 23208.

On the decay of crossing
numbers of sparse graphs
(with J. Balogh and J. Leaños). Journal of Graph Theory 80
(2015), 226251.

On the hardness of the joint crossing number (with
P. Hlineny). Lecture Notes in Computer Science 9472, Springer (2015), 603613.

Book embeddings of regular graphs
(with Jozsef Balogh). SIAM Journal in Discrete Mathematics 29 (2015), 811822.

Embedding a graphlike continuum in some surface
(with Robin Christian and Bruce Richter). Journal of Graph Theory
79 (2015), 159165.

Shellable drawings and the cylindrical crossing number of K_{ n }
(with Bernardo Ábrego, Oswin Aichholzer, Silvia
FernándezMerchant, and Pedro Ramos). Discrete and Computational
Geometry 52 (2014), 743753.

Book drawings of complete bipartite graphs
(with Etienne de Klerk and Dima Pasechnik). Discrete Applied
Mathematics 167 (2014), 8093.

The optimal drawings of K_{5,n} (with
C. HernándezVélez and C. Medina). Electronic Journal of
Combinatorics 21(4) (2014), #P4.1, 29 pp.

The 2page crossing
number of K_{n}
(with B. M. Ábrego, O. Aichholzer, S.
FernándezMerchant, and P. Ramos). Discrete and Computational
Geometry 49 (2013), 747777.

Zarankiewicz's Conjecture is finite for
each fixed m
(with R. Christian and R.B. Richter). Journal of Combinatorial Theory
Series B 103 (2013), 237247.

Large convex holes in
random point sets
(with J. Balogh and H. GonzálezAguilar). Comp. Geom. 46
(2013), 725733.

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 crossingcritical by
multiplying its edges
(with L. Beaudou and C. HernándezVélez). 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), 619633.

The
ErdősSós 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), 93100.

The rectilinear crossing
number of K_{n}: closing in (or are we?)
(with B. M. Ábrego and Silvia FernándezMerchant).
Thirty essays in Geometric Graph Theory
(János Pach, Ed.). Springer (2013), pp. 518.

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), 98108.

The 2page crossing number of
K_{n}
(with B. M. Ábrego, O. Aichholzer, S.
FernándezMerchant, and P. Ramos)
In 28th Ann.
ACM Symp. Computational Geometry, pp. 397403, Chapel Hill, NC, USA,
2012.

Nested cycles in large triangulations
and crossingcritical graphs (with C. HernándezVelez and R.
Thomas), Journal of Combinatorial Theory, 102 (2012), 8692.

On kedges, crossings, and
halving lines of geometric drawings of
K_{n} (with B. Abrego, M. Cetina,
S. FernándezMerchant, and J. Leaños), Discrete and
Computational Geometry, 48 (2012), 192215.

Visibilitypreserving
convexifications using singlevertex moves (with B. Abrego, M.
Cetina, and
J. Leaños), Information Processing Letters 112 (2012),
161173.

Stars and bonds in
crossingcritical graphs (with P. Hlineny), Journal of Graph
Theory 65 (2010), 198215.

The number of generalized
balanced lines (with D. Orden and P. Ramos), Discrete and
Computational Geometry 44 (2010), 805811.

3symmetric and 3decomposable geometric
drawings of K_{n} (with
B. Abrego, M. Cetina,
S. FernándezMerchant, and J. Leaños), Discrete
Applied Mathematics 158 (2010), 12401258.

The crossing number of a projective
graph is quadratic in the facewidth (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 kedges to generalized configurations of points and the
pseudolinear crossing number of
K_{n} (with
B. Ábrego, J. Balogh, S. FernándezMerchant, and J.
Leaños),
Journal of Combinatorial Theory, Series A 115 (2008), 12571264.

A central approach to bound
the number of crossings in a generalized configuration (with
B. Abrego, S. FernándezMerchant, and J. Leaños),
Electronic Notes in Discrete Mathematics 30 (2008) 273278.

The maximum number of halving
lines and the rectilinear crossing number of K_{n}
for n ≤ 27 (with
B. Abrego, S. FernándezMerchant, and J. Leaños),
Electronic Notes in Discrete Mathematics 30 (2008) 261266.

On the additivity of crossing
numbers of graphs
(with J. Leanos), Journal of Knot Theory and its
Ramifications 17 (2008), 10431050.

A note on harmonic subgraphs in
labelled geometric graphs (with G. Araujo, J. Balogh, R. Fabila,
and J. Urrutia), Information Processing Letters 105 (2008), 98102.

Simple Euclidean arrangements with
no
( &ge 5) gons are stretchable (with J. Leanos,
C. Merino, and J. Urrutia), Discrete and Computational Geometry
38 (2007), 595603.

On the crossing number of almost planar graphs (with P. Hlineny),
Lecture Notes in Computer Science 4372 (2007), 162173.

Large harmonious sets of noncrossing
edges for n randomly labeled
vertices in
convex position (with Jozsef Balogh and Boris Pittel), Random
Structures and Algorithms 30 (2007), 105130.

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), 155162.

Approximating the crossing number of toroidal graphs (with
P. Hlineny). Lecture Notes in Computer Science 4835 , 148159.
Springer, 2007.

On ksets, convex quadrilaterals, and the rectilinear crossing number
of
K_{n} (with Jozsef Balogh). Discrete and
Computational Geometry 35 (2006), 671690.
 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), 189202.
 Nearlylight
cycles in embedded graphs and crossingcritical graphs , (with
M. Lomeli), Journal
of Graph Theory 53 (2006), 151156..
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 `Nearlylight cycles in embedded graphs and
crossingcritical graphs'".

Two maps with large representativity on one surface (with B. Richter),
Journal of Graph Theory 50 (2005), 234245.
 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), 17911797.

Masterslave synchronization of
affine cellular
automaton pairs
(with E. Ugalde and J. Urias), Discrete and Continuous Dynamical Systems 13
(2005), no.
2, 491502.

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), 333341.
 On the crossing numbers of loop networks and Generalized
Petersen Graphs , Discrete Mathematics
302 (2005), no. 13, 243253.

Spanning trees of multicoloured point sets with few intersections
(with J. Leanos, C. Merino, and J. Urrutia),
Lecture Notes in Computer Science 3330 , SpringerVerlag,
Berlin, (2005), 113122.
 An improved bound for the crossing number of cr(C_{m}
X C_{ n}) : a selfcontained proof using mostly
combinatorial arguments (with E. Ugalde), Graphs and Combinatorics,
20 (2004), no. 2, 247253.
 Embedding grids in surfaces
(with Jim Geelen and Bruce Richter),
European Journal of Combinatorics 25 (2004), no. 6, 785792.
 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, 5372.

Morelia test:
improving the efficiency of the Gabriel test and face routing in
adhoc 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, SpringerVerlag,
Berlin, (2004), 2334.
 Small meshes of curves and their role in the analysis of
optimal meshes , Discrete Mathematics 263 (2003), no. 13,
233246.
 Optimal meshes of curves in the Klein bottle (with Hector A.
Juarez), Journal of Combinatorial Theory, Series B 88
(2003), no. 1, 185188.
 Infinite families of crossingcritical graphs with given average
degree, Discrete Mathematics, 271 (2003), no. 13, 343350.
 The Crossing Number of P(N,3) (with Bruce Richter), Graphs
and Combinatorics 18 (2002), no. 2, 381394.
 The Crossing Number of
C_{6} X C_{ n}
(with Bruce Richter), Australasian Journal of Combinatorics 23
(2001), 135144.
 Drawings of C_{m} X C_{n}
with one disjoint family II , Journal of Combinatorial Theory, Series
B, 82 (2001), no. 1, 161165.
 Bounding the crossing number of a graph in terms of the
crossing number of a minor with small maximum degree (with E.
GarciaMoreno), Journal of Graph Theory 36 (2001), no. 3,
168173.
 A lower bound for the Crossing Number of C_{ m}
X C_{n}, Journal of Graph Theory 35 (2000),
222226.
 On a crossing number result of Richter and Thomassen,
Journal of Combinatorial Theory, Series B, 79 (2000), no. 1,
9899.
 Drawings of C_{m} X C_{n}
with one disjoint family, Journal of Combinatorial Theory Series B,
76 (1999), no. 2, 129135.

On the Intersections of Systems of Curves, Journal of
Combinatorial Theory Series B, 75 (1999), no. 1, 5660.

On the Crossing Number of C_{m} X C_{n}
, Journal of Graph Theory 28 (1998), no. 3, 163170.
 Internal symmetries of cellular automata via their
polynomial representation (with J. Urias), Chaos 8 (1998), no.
3, 711716.
 Synchronization of cellular automaton pairs (with E.
Ugalde and
J. Urias), Chaos 8 (1998), no. 4, 814818.
 A cryptosystem based on cellular automata (with E. Ugalde
and J. Urias), Chaos 8 (1998), no. 4, 819822.
 Random perturbations of iterated maps (with J. Urias),
Journal of Mathematical Physics 37 (1996), no. 7, 36413643.
 Traveling patterns in cellular automata (with A. Enciso,
E. Ugalde
and J. Urias), Chaos 6 (1996), no. 3, 493503.
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 HernándezVélez (Ph.D., 2013)
 Sonia Rodríguez (M.Sc., 2015)
 Rodrigo Dorantes (M.Sc., 2015)
 Antonio Torres (M.Sc., in progress)
5~
 Carolina Medina (Ph.D., in progress)
Last modified: February 2017