Zentralblatt MATH  Publications of (and about) Paul Erdös
Zbl.No:  796.05049 Autor:  Erdös, Paul; Faudree, Ralph J.;
Rousseau, Cecil C. Title:  Extremal problems and generalized
degrees. (In English) Source:  Discrete Math. 127, No.1-3,
139-152 (1994). Review:  Authors' abstract: For a positive
integer n and a graphical property P, extn(P) will denote the
minimum number of edges in a graph G of order n that satisfies
property P, and Extn(P) will denote the class of graphs with n
vertices and extn(P) edges that have property P. The extremal
numbers extn(P) for properties P that have been commonly used as
sufficient conditions for Hamiltonian paths and cycles in graphs
will be investigated. In particular, results on the extremal
numbers for generalized degree and generalized independent
degree properties will be given, where for a fixed positive
integer t, the generalized degree \deltat(G) (generalized
independent degree \deltait(G)) is the minimum number of
vertices in the union of the neighborhoods of a set