$K_{2n+1}$ That Are $(2n+1)$-Color $n$ Sequentially Hamiltonian

Vites Longani, Hatairat Yingtaweesittikul

Abstract

It is known that $K_{2n+1}$ is the sum of n spanning cycles. We assign  colors  from $2n+1$ colors to each line of $K_{2n+1}$.   We find that, with some condition, it is possible to assign colors to  $K_{2n+1}$ 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.