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1998

On constructing snakes in powers of complete graphs

13 years 11 months ago
On constructing snakes in powers of complete graphs
We prove the conjecture of Abbott and Katchalski that for every m ≥ 2 there is a positive constant λm such that S(Kd mn) ≥ λmnd−1 S(Kd−1 m ) where S(Kd m) is the length of the longest snake (cycle without chords) in the cartesian product Kd m of d copies of the complete graph Km. As a corollary, we conclude that for any finite set P of primes there is a constant c = c(P) > 0 such that S(Kd n) ≥ cnd−1
Jerzy Wojciechowski
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where DM
Authors Jerzy Wojciechowski
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