Abstract
We show that every two-colouring of the edges of the complete graph K n ${K}_{n}$ contains a monochromatic trail or circuit of length at least 2 n 2 / 9 + o( n 2 ) $2{n}{2}\unicode{x02215}9+o({n}{2})$, which is asymptotically best possible.
We show that every two-colouring of the edges of the complete graph K n ${K}_{n}$ contains a monochromatic trail or circuit of length at least 2 n 2 / 9 + o( n 2 ) $2{n}{2}\unicode{x02215}9+o({n}{2})$, which is asymptotically best possible.