Ramsey-minimal graphs for star-forests

Stefan A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, R. H. Schelp

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

It is shown that if G and H are star-forests with no single edge stars, then (G, H) is Ramsey-finite if and only if both G and H are single stars with an odd number of edges. Further (Sm ∪kS1, Sn ∪tS1) is Ramsey-finite when m and n are odd, where Si denotes a star with i edges. In general, for G and H star-forests, (G∪kS1, H∪tS1) can be shown to be Ramsey-finite or Ramsey-infinite depending on the choice of G, H, k, and l with the general case unsettled. This disproves the conjecture given in [2] where it is suggested that the pair of graphs (L, M) is Ramsey-finite if and only if (1) either L or M is a matching, or (2) both L and M are star-forests of the type Sm ∪kS1, m odd and k ≥ 0.

Original languageEnglish
Pages (from-to)227-237
Number of pages11
JournalDiscrete Mathematics
Volume33
Issue number3
DOIs
Publication statusPublished - 1981

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Stars
Star
Graph in graph theory
Odd
If and only if
Disprove
Levenberg-Marquardt
Odd number
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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Burr, S. A., Erdős, P., Faudree, R. J., Rousseau, C. C., & Schelp, R. H. (1981). Ramsey-minimal graphs for star-forests. Discrete Mathematics, 33(3), 227-237. https://doi.org/10.1016/0012-365X(81)90266-1

Ramsey-minimal graphs for star-forests. / Burr, Stefan A.; Erdős, P.; Faudree, R. J.; Rousseau, C. C.; Schelp, R. H.

In: Discrete Mathematics, Vol. 33, No. 3, 1981, p. 227-237.

Research output: Contribution to journalArticle

Burr, SA, Erdős, P, Faudree, RJ, Rousseau, CC & Schelp, RH 1981, 'Ramsey-minimal graphs for star-forests', Discrete Mathematics, vol. 33, no. 3, pp. 227-237. https://doi.org/10.1016/0012-365X(81)90266-1
Burr, Stefan A. ; Erdős, P. ; Faudree, R. J. ; Rousseau, C. C. ; Schelp, R. H. / Ramsey-minimal graphs for star-forests. In: Discrete Mathematics. 1981 ; Vol. 33, No. 3. pp. 227-237.
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