I discussed here the problem of covering the *m*-fold complete graph on *n* vertices with copies of a given graph *G*.

The smallest strongly regular graph for which I don’t know the answer is the Shrikhande graph. I can copy 8.*K*_{16} with 20 copies of the Shrikhande graph, but perhaps one can do better.

**Problem:** Is it possible to cover 2.*K*_{16} with five copies of the Shrikhande graph?

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## About Peter Cameron

I count all the things that need to be counted.

Darryn Bryant has solved the Shrikhande challenge. He writes:

Here is the Shrikhande graph. Now, if you take the five images of this graph under powers of the permutation (X)(0 3 6 9 12)(1 4 7 10 13)(2 5 8 11 14), you cover the edges of the complete graph twice, as required.

Darryn also points out that Ben Fairbairn’s question has been answered in a paper by Peter Adams, Darryn E. Bryant and A. Khodkar, The spectrum problem for lambda-fold Petersen graph designs,

Journal of Combinatorial Mathematics and Combinatorial Computing34(2000), 159-176. The answer is,mK_{n}can always be partitioned into Petersen graphs as long asnis at least 10 and the obvious divisibility conditions (3 dividesm(n−1) and 15 dividesmn(n−1)/2) are satisfied, except for the single casem=1,n=10.