  An interval coloring of a graph G is a proper coloring of E(G) by positive
integers such that the colors on the edges incident to any vertex are
consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each
vertex of one part has degree 3 and each vertex of the other has degree 4; it
is unknown whether these all have interval colorings. We prove that G has an
interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a
spanning subgraph whose components are paths with endpoints at 3-valent
vertices and lengths in {2,4,6,8}. We provide sufficient conditions for the
existence of such a subgraph.
