Upper (sharp!) Bound of 2 on Erdős Number (2007)

  1. P. Erdős, Z. Füredi, R. J. Gould, and D. S. Gunderson, Extremal graphs for intersecting triangles. J. Combin. Theory Ser. B, 64 (1995), no. 1, 89--100.
  2. Michael Ferrara, Ronald J. Gould, and Stephen Hartke, The structure and existence of 2-factors in iterated line graphs. Discuss. Math. Graph Theory, 27 (2007), no. 3, 507--526.

Upper Bound of 4 on Erdős Number (2004)

  1. Paul Erdős and Ron Graham, "On packing squares with equal squares," J. Combinatorial Theory Ser. A 19 (1975), 119-123.
  2. Persi Diaconis, Ron Graham, and Bernd Sturmfels, "Primitive partition identities," Combinatorics, Paul Erdős is eighty, Vol. 2 (Keszthely, 1993), 173-192, Bolyai Soc. Math. Stud., 2, Janos Bolyai Math. Soc., Budapest, 1996.
  3. Mike Develin and Bernd Sturmfels, "Tropical convexity," Doc. Math. 9 (2004), 1-27 (electronic).
  4. Mike Develin, Stephen G. Hartke, and David Petrie Moulton, "A general notion of visibility graphs," Discrete and Computational Geometry, 29 (2003), no. 4, 511-524.

Upper Bound of 5 on Erdős Number (2003)

  1. Paul Erdős and Fred Galvin, "Monochromatic infinite paths," Discrete Math., 113 (1993), no. 1-3, 59-70.
  2. George M. Bergman and Fred Galvin, "Transversals of families in complete lattices, and torsion in product modules," Order, 3 (1987), no. 4, 391-403.
  3. G.M. Bergman and I.M. Isaacs, "Rings with fixed-point-free group actions," Proc. London Math. Soc. (3), 27 (1973), 69-87.
  4. I.M. Isaacs and David Petrie Moulton, "Real fields and repeated radical extensions," J. Algebra, 201 (1998), no. 2, 429-455.
  5. Mike Develin, Stephen G. Hartke, and David Petrie Moulton, "A general notion of visibility graphs," Discrete and Computational Geometry, 29 (2003), no. 4, 511-524.

A different path using conference proceedings: (2000)
  1. Leon Bankoff, Paul Erdős, and Murray S. Klamkin, "The Asymmetric Propeller," Mathematics Magazine, 46 (1973), 270-272.
  2. Roberto W. Frucht and Murray S. Klamkin, "On Best Quadratic Triangle Inequalities," Geometriae Dedicata, 2 (1973), 341-348.
  3. Roberto W. Frucht and Joseph A. Gallian, "Labeling prisms," Ars Combinatoria, 26 (1988), 69-82.
  4. Joseph A. Gallian and Aparna W. Higgins, "Helping Students Present Their Research," Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, J.A. Gallian, ed., American Mathematical Society (2000), 289-295.
  5. Stephen G. Hartke and Aparna W. Higgins, "Maximum Degree Growth of the Iterated Line Graph," The Electronic Journal of Combinatorics, 6 (1999), #R28.

Upper Bound of 6 on Erdős Number (1999)

  1. Paul Erdős and Andrew M. Odlyzko, "On the Density of Odd Integers of the Form (p-1)/2k and Related Questions," Journal of Number Theory, 11 (1979), 257-263.
  2. Edward A. Bender, Andrew M. Odlyzko, and Richmond L. Bruce, "The Asymptotic Number of Irreducible Partitions," European Journal of Combinatorics, 6 (1985), no. 1, 1-6.
  3. Edward A. Bender and Jon T. Butler, "Enumeration of Structured Flowcharts," Journal of the ACM, 32 (1985), no. 3, 537-548.
  4. Jon T. Butler, David S. Herscovici, Tsutomu Sasao, and Robert J. Barton, III, "Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions," IEEE Transactions on Computers, 46 (1997), no. 4, 491-494.
  5. David S. Herscovici and Aparna W. Higgins, "The Pebbling Number of C5xC5," Discrete Mathematics, 187 (1998), 123-135.
  6. Stephen G. Hartke and Aparna W. Higgins, "Maximum Degree Growth of the Iterated Line Graph," The Electronic Journal of Combinatorics, 6 (1999), #R28.

To learn more about Erdős Numbers, visit the Erdős Number Project home page.
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