Carlos A. Alfaro


Carlos Alejandro Alfaro Montúfar

Banco de México

alfaromontufar [at] gmail [dot] com
carlos [dot] alfaro [at] banxico [dot] org [dot] mx 

Research Interests

Algebraic Combinatorics, Topological Graph Theory and Optimization

Short Bio

Since 2014, I am researcher at BANXICO (the Central Bank of Mexico), where my principal activities consist in developing and implementing optimization models. Between 2011 and 2012, I visited the HP Labs at Palo Alto, CA to work with Burcu AydinKemal GulerLyle RamshawPano Santos and Bob Tarjan. There, we developed algorithms to study tree-structure data, and supported the development of assignment algorithms for resource planning allocation.

I received my Ph.D. degree in 2014 from the Department of Mathematics at CINVESTAV under supervision of Carlos E. Valencia. Since then, I started my research on Algebraic Combinatorics and Discrete Applied Mathematics. In particular, I focus on algebraic invariants of graphs such as Laplacian matrices, sandpile groups and critical ideals. 

Extended CV

Journal Papers

Algebraic combinatorics
Graph classes for critical ideals, minimum rank and zero forcing number, submitted.

Distance ideals of graphs (with L. Taylor) submitted.

Critical ideals, minimum rank and zero forcing number (with Jephian C.-H. Lin) submitted.

On two-quotient strong starters for F_q (with Christian Rubio-Montiel and Adrián Vázquez-Ávila) accepted in Utilitas Mathematica.

Digraphs with at most one trivial critical ideal (with Carlos E. Valencia & Adrián Vázquez-Ávila) in Linear and Multilinear Algebra, 2017. []

Critical ideals of graphs with twin vertices (with H. H. Corrales & Carlos E. Valencia) in Advances in Applied Mathematics, 2017 [].

Graphs with two trivial critical ideals (with C. E. Valencia), in Discrete Applied Mathematics, 2014. []

On the sandpile group of the cone of a graph (with C. E. Valencia), in Linear Algebra and its Applications, 2012. []

Operations Research

Optimizing the production cost of minting with mixed integer programming (with J. Aguilera, C. Guadarrama, R. Martinez-Noriega & A. Sanchez-Flores) submitted.

Dimension Reduction in Principal Component Analysis for Trees (with B. Aydin, E. Bullitt, A. Ladha, and C. E. Valencia), in Computational Statistics & Data Analysis, 2014. []

Graph theory

The crossing number of the cone of a graph (with Alan Arroyo, Marek Derňár and Bojan Mohar) submitted.

Covering and 2-packing numbers in graphs (with Christian Rubio-Montiel and Adrián Vázquez-Ávila) submitted.

Linear systems

On linear systems in which the transversal number equals the 2–packing number (with G. Araujo-Pardo, C. Rubio-Montiel, A. Vázquez-Avila) submitted.

On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed (with A. Vázquez-Ávila) submitted.

Conference papers

Graphs with few trivial critical ideals (with Carlos E. Valencia), in Electronic Notes in Discrete Mathematics, 2015. Presented in LAGOS'15.

The crossing number of the cone of a graph (with Alan Arroyo, Marek Derňár and Bojan Mohar), in Lecture Notes in Computer Science vol. 9801, 2016. Presented in Graph Drawing'16 by Bojan Mohar (slides).

Ciritcal ideals of digraphs (with Carlos E. Valencia and Adrián Vázquez-Ávila) accepted in Matemática Contemporânea. Presented  in VII Latin American Workshop on Cliques in Graphs, November 8-11 2016.


Selection of data paths. US Patent Application. Ref. 83037389. (with B. Aydin, K. Guler, C. E. Valencia) Hewlett-Packard Company, 2012.


Knotj3d. INDAUTOR Reg. 03-2007-100314141100-01 (with O. Gutú and R. Lopéz-Hérnandez) 2007.


JGraphs  -  (github) A code in Java that serves as a graphical interface for computing the critical group and the critical ideals of a digraph. It requires Sage and Emacs. But if wanted, the code can be modified to use an alternative Computer Algebra System (a previous version used Mathematica and Macaulay2) or Text Editor. This also can be used to export in Tikz format the rectilinear drawing of the graph.

CSandPile - (github) CSandPile is a tool developed in C++ for computing the group operations of the recurrent representatives of non-negative configurations of a graph. It helps to understand the combinatorial structure of the group operations of the recurrent configurations that generate the sandpile group of a graph.

RiceRocks  -  (github) (It doesn't work on Internet Explorer) Just push play. Enjoy and modify! I coded a version for Android watch it here.

KnotJ3D - (github) This is a Java applet, which draws 3D tangles. There are implemmented some operations like sum and closure. It was coded in Java3D, so you need to install it to run it.

Recent presentations

Interesting readings

           Mathematics and Programming in the Cloud with CoCalc

         Nature of Code

        IFORS Developing Countries On-Line Resources page "Operational Research" (OR) is the discipline of applying advanced analytical methods to help make better decisions. By using techniques such as problem structuring methods and mathematical modelling to analyze complex situations, Operational Research gives executives the power to make more effective decisions and build more productive systems.