##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 465.05058

**Autor: ** Erdös, Paul; Faudree, Ralph J.; Rousseau, C.C.; Schelp, R.H.

**Title: ** Graphs with certain families of spanning trees. (In English)

**Source: ** J. Comb. Theory, Ser. B 32, 162-170 (1982).

**Review: ** In this paper, sufficient conditions are given in terms of \delta(G) and \Delta(T), for a graph G with n vertices to contain a tree T with n vertices. One of these sufficient conditions is used to calculate some of the Ramsey numbers for the pair tree-star. Also necessary conditions are given, in terms of \delta(G), for a graph G with n vertices to contain all trees with n vertices.

**Classif.: ** * 05C75 Structural characterization of types of graphs

05C05 Trees

05C55 Generalized Ramsey theory

**Keywords: ** Ramsey numbers

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag