Abstract :
In this paper we completely characterise the family of eulerian simple graphs G with maximum degree at most 4 which admit a triangle-free eulerian tour, i.e., a sequence v1v2…vmv1 such that each vi is a vertex, the pairs vi, vi + 1, i = 1,2,…,m are the m distinct edges in G and finally, vi + 3 ≠ vi for all i = 1,2,…, m, with indices counted modulo m.
