Subgraphs of minimal degree k

P. Erdős, R. J. Faudree, C. C. Rousseau, R. H. Schelp

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

For k ≥ 2, any graph G with n vertices and (k-1)(n-k+2)+( 2 k-2) edges has a subrgraph of minimum degree at least k; however, this subgraph need not be proper. It is shown that if G has at least (k-1)(n-k+2)+( 2 k-2)+1 edges, then there is a subgraph H of minimal degree k that has at most n - √n ;√6k 3 vertices. Also, conditions that insure the existense of smaller subgraphs of minimum degree k are given.

Original languageEnglish
Pages (from-to)53-58
Number of pages6
JournalDiscrete Mathematics
Volume85
Issue number1
DOIs
Publication statusPublished - Nov 1 1990

    Fingerprint

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Erdős, P., Faudree, R. J., Rousseau, C. C., & Schelp, R. H. (1990). Subgraphs of minimal degree k. Discrete Mathematics, 85(1), 53-58. https://doi.org/10.1016/0012-365X(90)90162-B