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 Joseph Mitchell:
Zhong Sichen, Lu Zhao, Yan Liang, Mohammadzaman Zamani, Rob Patro, Rezaul Chowdhury, Esther Arkin, Joseph Mitchell, and Steven Skiena, "Optimizing Read Reversals for Sequence Compression (Extended Abstract)", Proceedings of the 15th International Workshop on Algorithms in Bioinformatics (WABI 2015), Atlanta, GA, LNCS 9289, pp. 189-202, 2015.
      2. Joseph Mitchell collaborated with Craig Tovey:
Sven Koenig, Joseph Mitchell, Apurva Mudgal, and Craig Tovey, "A near-tight approximation algorithm for the robot localization problem", SIAM Journal on Computing, vol. 39 (2), pp. 461490, 2009.
      1. Craig Tovey collaborated with Paul Erdös:
Neil Calkin, Paul Erdös, and Craig Tovey, "New Ramsey bounds from cyclic graphs of prime order", SIAM Journal on Discrete Mathematics, vol. 10(3), pp. 381387, 1997.