Information about Erdös number facts can be found on The Erdös Number Project web page. Here are a few Erdös number and related facts about me.
There are 509 people with an Erdos number of 1. My Erdös number is equal to 1, as a consequence of the following paper: P. Erdös, R. C. Mullin, V. Sos, and D. R. Stinson, Finite linear spaces and projective planes, Discrete Math. 47 (1983), 49-62.
The collaboration graph of the second kind joins two authors by an edge if they have co-authored a two-author paper. The "k-core" of a graph is the (unique) largest subgraph all of whose vertices have degree at least k. The largest k for which the collaboration graph of the second kind has a non-empty k-core is k=5. This 5-core is called the "main core" of the collaboration graph of the second kind. There are 70 people in the main core, one of which is me. In fact, there are 19 design theorists in the main core: Billington, Colbourn, Hartman, Heinrich, P. Hoffman, Horak, Kreher, Lindner, E. Mendelsohn, Mullin, Phelps, Rees, Rodger, Rosa, Stanton, Stinson, Vanstone, Wallis, Zhu.
Paul Erdös asked if the collaboration graph of the second kind is planar. It is not. In fact, there are exactly four occurrences of complete graphs of order five in the main core of the collaboration graph of the second kind. One of them is Lindner-Mullin-Rosa-Stinson-Wallis.
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