  An edge-coloring of a multigraph G with colors 1,2,...,t is called an
interval t-coloring if all colors are used, and the colors of edges incident to
any vertex of G are distinct and form an interval of integers. In this paper we
prove that if G is a connected cubic multigraph (a connected cubic graph) that
admits an interval t-coloring, then t\leq |V(G)| +1 (t\leq |V(G)|), where V(G)
is the set of vertices of G. Moreover, if G is a connected cubic graph, G\neq
K_{4}, and G has an interval t-coloring, then t\leq |V(G)| -1. We also show
that these upper bounds are sharp. Finally, we prove that if G is a bipartite
subcubic multigraph, then G has an interval edge-coloring with no more than
four colors.
