Cycle-saturated graphs of minimum size

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

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18 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
DOIs
Publication statusPublished - Apr 6 1996

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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. https://doi.org/10.1016/0012-365X(95)00173-T