Extremal problems and generalized degrees

P. Erdős, Ralph J. Faudree, Cecil C. Rousseau

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

For a positive integer n and a graphical property P, extn(P) will denote the minimal number of edges in a graph G of order n that satisfies property P, and Ext>n(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 the generalized degree and generalized independent degree properties will be given, where for a fixed positive integer t, the generalized degree δt(G) (generalized independent degree δit(G)) is the minimum number of vertices in the union of the neighborhoods of a set of t (independent) vertices of the graph G.

Original languageEnglish
Pages (from-to)139-152
Number of pages14
JournalDiscrete Mathematics
Volume127
Issue number1-3
DOIs
Publication statusPublished - Mar 15 1994

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Hamiltonians
Extremal Problems
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Hamiltonian path
Integer
Hamiltonian circuit
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Sufficient Conditions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Extremal problems and generalized degrees. / Erdős, P.; Faudree, Ralph J.; Rousseau, Cecil C.

In: Discrete Mathematics, Vol. 127, No. 1-3, 15.03.1994, p. 139-152.

Research output: Contribution to journalArticle

Erdős, P. ; Faudree, Ralph J. ; Rousseau, Cecil C. / Extremal problems and generalized degrees. In: Discrete Mathematics. 1994 ; Vol. 127, No. 1-3. pp. 139-152.
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