Cycle-saturated graphs of minimum size

C. A. Barefoot, L. H. Clark, R. C. Entringer, T. D. Porter, L. A. Székely, Z. Tuza

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A graph G is called Ck-saturated if G contains no cycles of length k but does contain such a cycle after the addition of any new edge. Bounds are obtained for the minimum number of edges in Ck-saturated graphs for all k ≠ 8 or 10 and n sufficiently large. In general, it is shown that the minimum is between n + 1 c1n/k and n + c2n/k for some positive constants c1 and c2. Our results provide an asymptotic solution to a 15-year-old problem of Bollobás.

Original languageEnglish
Pages (from-to)31-48
Number of pages18
JournalDiscrete Mathematics
Volume150
Issue number1-3
Publication statusPublished - Apr 6 1996

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Cycle
Asymptotic Solution
Graph in graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Barefoot, C. A., Clark, L. H., Entringer, R. C., Porter, T. D., Székely, L. A., & Tuza, Z. (1996). Cycle-saturated graphs of minimum size. Discrete Mathematics, 150(1-3), 31-48.

Cycle-saturated graphs of minimum size. / Barefoot, C. A.; Clark, L. H.; Entringer, R. C.; Porter, T. D.; Székely, L. A.; Tuza, Z.

In: Discrete Mathematics, Vol. 150, No. 1-3, 06.04.1996, p. 31-48.

Research output: Contribution to journalArticle

Barefoot, CA, Clark, LH, Entringer, RC, Porter, TD, Székely, LA & Tuza, Z 1996, 'Cycle-saturated graphs of minimum size', Discrete Mathematics, vol. 150, no. 1-3, pp. 31-48.
Barefoot CA, Clark LH, Entringer RC, Porter TD, Székely LA, Tuza Z. Cycle-saturated graphs of minimum size. Discrete Mathematics. 1996 Apr 6;150(1-3):31-48.
Barefoot, C. A. ; Clark, L. H. ; Entringer, R. C. ; Porter, T. D. ; Székely, L. A. ; Tuza, Z. / Cycle-saturated graphs of minimum size. In: Discrete Mathematics. 1996 ; Vol. 150, No. 1-3. pp. 31-48.
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