My Erdös Number is 3. Here is how (obtained from AMS Collaboration Distance Calculator):

      3. I collaborated with Mikkel Thorup:
Camil Demetrescu, Mikkel Thorup, Rezaul Alam Chowdhury, and Vijaya Ramachandran, "Oracles for Distances Avoiding a Failed Node or Link", SIAM Journal on Computing, vol. 37 (5), pp. 1299-1318, 2008.
      2. Mikkel Thorup collaborated with Peter Mann Winkler:
Mike Paterson, Yuval Peres, Mikkel Thorup, Peter Winkler, and Uri Zwick, "Maximum Overhang (extended abstract)", Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 756-765, 2008.
      1. Peter Mann Winkler collaborated with Paul Erdös:
Paul Erdös, Pavol Hell, and Peter Winkler, "Bandwidth versus Bandsize", Graph theory in memory of G. A. Dirac (Sandbjerg, 1985), pp. 117-129, Ann. Discrete Math., 41, North-Holland, Amsterdam, 1989.

Here is another sequence.

      3. I collaborated with Phillip Gibbons:
Guy Blelloch, Rezaul Alam Chowdhury, Phillip Gibbons, Vijaya Ramachandran, Shimin Chen, and Michael Kozuch, "Provably Good Multicore Cache Performance for Divide-and-Conquer Algorithms", Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 501-510, 2008.
      2. Phillip Gibbons collaborated with Márió Szegedy:
Noga Alon, Phillip Gibbons, Yossi Matis, and Márió Szegedy, "Tracking Join and Self-join Sizes in Limited Storage", Journal of Computer and System Sciences (Special Issue on PODS 1999), vol. 64 (3), pp. 719-747, 2002.
      1. Márió Szegedy collaborated with Paul Erdös:
Paul Erdös, Péter Pálfy, and Márió Szegedy, "a (mod p) ≤ b (mod p) for all primes p implies a = b", American Mathematical Monthly, 94(2): 169-170, 1987.

Yet another one.

      3. I collaborated with Mikkel Thorup:
Camil Demetrescu, Mikkel Thorup, Rezaul Alam Chowdhury, and Vijaya Ramachandran, "Oracles for Distances Avoiding a Failed Node or Link", SIAM Journal on Computing, vol. 37 (5), pp. 1299-1318, 2008.
      2. Mikkel Thorup collaborated with Noga Alon:
Noga Alon, Nick Duffield, Carsten Lund and Mikkel Thorup, "Estimating Arbitrary Subset Sums with Few Probes", Proceedings of the 24th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS 2005), pp. 317-325, 2005.
      1. Noga Alon collaborated with Paul Erdös:
Noga Alon and Paul Erdös, "Disjoint Edges in Geometric Graphs", Discrete & Computational Geometry, 4: 287-290, 1989.