### Abstract

Let G be a connected graph on n vertices with no more than n(\ + e) edges, and P_{k}or C_{k}a path or cycle with k vertices. In this paper we will show that if n is sufficiently large and e is sufficiently small then for k odd r(G> C_{k}) = In - 1. Also, for k > 2, r(G, p_{k}) _ max(n + [k/2] — 1, n + k - 2 — α' - δ), where a' is the independence number of an appropriate subgraph of G and 6 is 0 or 1 depending upon /t, k and a.

Original language | English |
---|---|

Pages (from-to) | 501-512 |

Number of pages | 12 |

Journal | Transactions of the American Mathematical Society |

Volume | 269 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1982 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*269*(2), 501-512. https://doi.org/10.1090/S0002-9947-1982-0637704-5

**Ramsey numbers for the pair sparse graph-path or cycle.** / Burr, S. A.; Erdős, P.; Faudree, R. J.; Rousseau, C. C.; Schelp, R. H.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 269, no. 2, pp. 501-512. https://doi.org/10.1090/S0002-9947-1982-0637704-5

}

TY - JOUR

T1 - Ramsey numbers for the pair sparse graph-path or cycle

AU - Burr, S. A.

AU - Erdős, P.

AU - Faudree, R. J.

AU - Rousseau, C. C.

AU - Schelp, R. H.

PY - 1982

Y1 - 1982

N2 - Let G be a connected graph on n vertices with no more than n(\ + e) edges, and Pkor Cka path or cycle with k vertices. In this paper we will show that if n is sufficiently large and e is sufficiently small then for k odd r(G> Ck) = In - 1. Also, for k > 2, r(G, pk) _ max(n + [k/2] — 1, n + k - 2 — α' - δ), where a' is the independence number of an appropriate subgraph of G and 6 is 0 or 1 depending upon /t, k and a.

AB - Let G be a connected graph on n vertices with no more than n(\ + e) edges, and Pkor Cka path or cycle with k vertices. In this paper we will show that if n is sufficiently large and e is sufficiently small then for k odd r(G> Ck) = In - 1. Also, for k > 2, r(G, pk) _ max(n + [k/2] — 1, n + k - 2 — α' - δ), where a' is the independence number of an appropriate subgraph of G and 6 is 0 or 1 depending upon /t, k and a.

UR - http://www.scopus.com/inward/record.url?scp=84968493692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968493692&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1982-0637704-5

DO - 10.1090/S0002-9947-1982-0637704-5

M3 - Article

AN - SCOPUS:84968493692

VL - 269

SP - 501

EP - 512

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -