EDIT (2023-12-31): A decade into my academic career, my Erdős Number is even smaller now.

EDIT (2014-01-08): It appears as though my Erdős Number is smaller than I first thought. Thanks Barry (my PhD supervisor) for your vanity.

Paul Erdős was a very prolific mathematician, and, although technically homeless, he lived with his collaborators, with his famous initial greeting "my mind is open", during their work together. When finished, he moved to the house of another collaborator. He thought of mathematical research as a social event.

As a type of homage, with some admitted humility from Erdős himself, friends of his gave themselves an "Erdős Number" that measured the "collaborative distance" from him. Erdős has the number 0 (and the only that has it), people that have co-authored with him have the number 1, co-authors of co-authors of Erdoős have the number 2, and so on. There's more information in the Wikipedia article on Erdős Number.

In any case, apparently I have one. In the following list of publications, the numbers in brackets are the author's corresponding Erdős number:

Aharoni, R.[1]; Erdős, P.[0]; Linial, N.; Optima of dual integer linear programs. Comb. 8(1): 13-20 (1988).

Aharoni, R.[1]; Herman, G.[2]; Kuba, A.; Binary vectors partially determined by linear equation systems. Discrete Mathematics. 171(1-3): 1-16 (1997).

Ceja, C.; Rascon, C.[3]; Garduño, E.; Carvalho, B; Herman, G.[2]; Smooth normals with blobs for surfaces from 3D binary images. Topology Proceedings. 61(2023): 239-267 (2022).

So, my Paul Erdős number is now 3. I think this the best I'll do; quite well though.

EDIT (2023-12-31): A decade before, a decade after. Two jumps. Not bad.

Borosh, I.; Chui, Charles K.[1]; Erdős, P. [0];, On changes of signs in infinite series. (Russian summary), Anal. Math. 4 (1978), no. 1, 3–12.

Chen, Guang Rong[1]; Chui, Charles K.[2], Design of near-optimal linear digital tracking filters with colored input., J. Comput. Appl. Math. 15 (1986), no. 3, 353–370.

Guan, Zhi-Hong; Chan, C. W.; Leung, Andrew Y. T.[3]; Chen, Guan Rong[2], Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations. (English summary), IEEE Trans. Circuits Systems I Fund. Theory Appl. 48 (2001), no. 8, 1011–1019.

Wang, X., Lennox, B.[4], Goulding, P.R. and Leung, Andrew Y.T.[3], (2000), ‘Practical application of principal component analysis’, Proceedings of the Chinese Control Conference, Honk Kong University, 595-599

Rascon, C. [5]; Lennox, B. [4]; Marjanovic, O. Recovering Independent Components from Shifted Data using FastICA and Swarm Intelligence. Applied Spectroscopy 63(10), Oct. 2009.

So, my Paul Erdős number is 5. Better.

EDIT (2014-01-14): Yet another way to get to the same number.

Alon, Noga[1]; Erdős, P[0]. An application of graph theory to additive number theory. European J. Combin. 6 (1985), no. 3, 201–203.

Alon, Noga[1]; Bradford, Phillip G.; Fleischer, Rudolf[2]. Matching nuts and bolts faster. Inform. Process. Lett. 59 (1996), no. 3, 123–127.

Fleischer, Rudolf[2]; Koga, Hisashi[3]. Balanced scheduling toward loss-free packet queueing and delay fairness. Twelfth Annual International Symposium of Algorithms and Computation. Algorithmica 38 (2004), no. 2, 363–376.

Fuentes, Gibran[4]; Koga, Hisashi[3]; Watanabe, Toshinori. Unsupervised Object Discovery from Images by Mining Local Features Using Hashing. Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications Lecture Notes in Computer Science Volume 5856, 2009, pp 978-985.

Pineda, Luis; Salinas, Lisset; Meza, Ivan; Rascon, Caleb[5]; Fuentes, Gibran[4]. SitLog: A Programming Language for Service Robot Tasks. International Journal of Advanced Robotic Systems, 2013, 10:538.

OLD LIST

Erdős, P. [0]; Gerencsér, L.[1]; Máté, A.
Problems of graph theory concerning optimal design. Combinatorial theory and its applications, I (Proc. Colloq., Balatonfüred, 1969), pp. 317–325. North-Holland, Amsterdam, 1970.

Gerencsér, László [1]; Rissanen, Jorma [2]
Asymptotics of predictive stochastic complexity. New directions in time series analysis, Part II, 93–112,
IMA Vol. Math. Appl., 46, Springer, New York, 1993.

Rissanen, J. [2]; Ljung, L. [3]
Estimation of optimum structures and parameters for linear systems. Mathematical systems theory (Proc. Internat. Sympos., Internat. Centre Mech. Sci., Udine, 1975), pp. 92–110. Lecture Notes in Econom. and Math. Systems, 131. Springer, Berlin, 1976.

Hagenblad, Anna; Ljung, Lennart [3]; Wills, Adrian [4]
Maximum likelihood identification of Wiener models. Automatica J. IFAC 44 (2008), no. 11, 2697–2705.

Heath, W. P. [5]; Wills, A. G. [4]
Design of a cross-directional controllers with optimal steady state performance. Eur. J. Control 10 (2004), no. 1, 15–29.

Li, G.; Heath, W. P. [5]; Lennox, B. [6]
Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program. IET Control Theory Appl. 2 (2008), no. 7, 554–563.

Rascon, C. [7]; Lennox, B. [6]; Marjanovic, O.
Recovering Independent Components from Shifted Data using FastICA and Swarm Intelligence. Applied Spectroscopy 63(10), Oct. 2009.

So, my Paul Erdős number is 7. Not bad, I suppose.