### Abstract

Chvátal has shown that if T is a tree on n points then r(K_{k}, T) = (k – 1) (n – 1) + 1, where r is the (generalized) Ramsey number. It is shown that the same result holds when T is replaced by many other graphs. Such a T is called k‐good. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense, is k‐good.

Original language | English |
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Pages (from-to) | 39-51 |

Number of pages | 13 |

Journal | Journal of Graph Theory |

Volume | 7 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*7*(1), 39-51. https://doi.org/10.1002/jgt.3190070106

**Generalizations of a Ramsey‐theoretic result of chvátal.** / Burr, Stefan A.; Erdős, P.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 7, no. 1, pp. 39-51. https://doi.org/10.1002/jgt.3190070106

}

TY - JOUR

T1 - Generalizations of a Ramsey‐theoretic result of chvátal

AU - Burr, Stefan A.

AU - Erdős, P.

PY - 1983

Y1 - 1983

N2 - Chvátal has shown that if T is a tree on n points then r(Kk, T) = (k – 1) (n – 1) + 1, where r is the (generalized) Ramsey number. It is shown that the same result holds when T is replaced by many other graphs. Such a T is called k‐good. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense, is k‐good.

AB - Chvátal has shown that if T is a tree on n points then r(Kk, T) = (k – 1) (n – 1) + 1, where r is the (generalized) Ramsey number. It is shown that the same result holds when T is replaced by many other graphs. Such a T is called k‐good. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense, is k‐good.

UR - http://www.scopus.com/inward/record.url?scp=0003030478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003030478&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190070106

DO - 10.1002/jgt.3190070106

M3 - Article

AN - SCOPUS:0003030478

VL - 7

SP - 39

EP - 51

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -