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

--------------------------------------------------- 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 -------------------------------------------------- "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)