  A simple graph is triangular if every edge is contained in a triangle. A
sequence of integers is graphical if it is the degree sequence of a simple
graph. Egan and Nikolayevsky recently conjectured that every graphical sequence
whose terms are all at least 4 is the degree sequence of a triangular simple
graph, and proved this in some special cases. In this paper we state and prove
the analogous version of this conjecture for multigraphs.
