Note Universal Caterpillars

For a class V of graphs, denote by a(@?) the least value of m so that for some graph II on m vertices, every GE Q occurs as a subgraph of U. In this note we obtain rather sharp bounds on u(q) when Q is the class of caterpillars on n vertices, i.e., tree with property that the vertices of degree exceeding one induce a path. Recently several of the authors have investigated graphs U(g) which are " universal " with respect to various classes Q of graphs. By this we mean that every graph G E 59 occurs as a subgraph of U(V). The usual goal has been to estimate u(g), the minimum number of edges such a universal graph U(g) can have. Typical examples of known results are: (i) @I = {trees on n vertices},