K<inf>2n+1</inf> that are (2n + 1)-color n sequentially hamiltonian

Abstract

It is known that K2n+1 is the sum of n spanning cycles. We assign colors from 2n + 1 colors to each line of K2n+1 . We find that, with some condition, it is possible to assign colors to K2n+1 such that each point is adjacent to 2n lines of different colors and each of n hamiltonian cycles has 2n + 1 lines of different colors.