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mod != %

• To: mathgroup at yoda.physics.unc.edu
• Subject: mod != %
• From: fulling at sarastro.math.tamu.edu (Stephen A. Fulling)
• Date: Sun, 10 Oct 93 16:35:36 CDT

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Milan, 7 Oct. 93

 Hi, I am reading a book on "Graph Theory" by Harary.

I am interested in the "Turan" theorem which state that
the maximum number of edges a graph with p points can have
without containing a complete subgraph of n vertices (i.e. Kn)
is given by the formula:  ( page 18)

	   (n-2)(p^2 - r^2)
ex(p,Kn) = ---------------- + Binomial[r,2]  with  (n<=p)
	       2(n-1)

where p = r mod(n-1) and (0<= r <n-1)

Now "p" is at most equal to n-2 which seems to contradict the entire
formula.

Can anybody help me understand if there is a typo error or something
else?

	Thanks Anyway

Alberto Puglisi
Italtel R&D
Milan, Italy            Internet:   puglisi at settimo.italtel.it

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"p = r mod(n-1) and (0<= r <n-1)" means "r = p % (n-1)" (in C).

This is the mathematician's "mod", not the computer programmer's "mod"
or "%".  It states a relation among p, r, and n, not a function p of r
and n.

For example, if n-1 = 4 and p = 102 and r = 2, then p = r mod(n-1).

Of course, p must be >= n (as stated) for the theorem to have any
meaning.

				     Steve Fulling
				     Texas A&M Math
				     (but not a graph theorist)