Name
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 (S\"m @?kS\"1, S\"n @?tS\"1) is Ramsey-finite when m and n are odd, where S\"i denotes a star with i edges. In general, for G and H star-forests, (G@?kS\"1, H@?tS\"1) 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 S\"m @?kS\"1, m odd and k = 0. |
Year | DOI | Venue |
|---|---|---|
1981 | 10.1016/0012-365X(81)90266-1 | Discrete Mathematics |
Field | DocType | Volume |
Discrete mathematics,Graph,Combinatorics,Stars,Parity (mathematics),Conjecture,Mathematics | Journal | 33 |
Issue | ISSN | Citations |
3 | Discrete Mathematics | 8 |
PageRank | References | Authors |
2.16 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stefan A. Burr | 1 | 110 | 32.22 |
| P Erdös | 2 | 626 | 190.85 |
| R.J. Faudree | 3 | 189 | 42.73 |
| C.C Rousseau | 4 | 29 | 8.57 |
| Richard H. Schelp | 5 | 274 | 61.72 |