The conjecture cr(C_m\times C_n)=(m-2)n is true for all but finitely many n, for each m
Abstract
Description
It has been long congectured that the crossing number of $C_m\times C_n$ is $(m-2)n$ for $2<m<=n$. In this paper we proved that conjecture is true for all but finitely many $n$ for each $m$. More specifically we proved conjecture for $n>=(m/2)((m+3)^2/2+1)$.The proof is largely based on the theory of arrangements introduced by Adamsson and further developed by Adamsson and Richter.
16 pages, plainTeX, to be subnitted to "J. of Graph Theory"
16 pages, plainTeX, to be subnitted to "J. of Graph Theory"