ISSN:0364-9024    

DOI:10.1002/jgt.3190070102

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

ISSN:0364-9024    

DOI:10.1002/jgt.3190070103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractAn anecdotal account of some of the events and people that have helped shape Ramsey Theory.

ISSN:0364-9024    

DOI:10.1002/jgt.3190070104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractThis paper is a survey of the methods used for determining exact values and bounds for the classical Ramsey numbers in the case that the sets being colored are two‐element sets. Results concerning the asymptotic behavior of the Ramsey functionsR(k,l) andRm(k) are also give

ISSN:0364-9024    

DOI:10.1002/jgt.3190070105

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractChvátal has shown that ifTis a tree onnpoints thenr(Kk, T) = (k– 1) (n– 1) + 1, whereris the (generalized) Ramsey number. It is shown that the same result holds whenTis replaced by many other graphs. Such aTis calledk‐good. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense, is

ISSN:0364-9024    

DOI:10.1002/jgt.3190070106

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractA table of the size Ramsey number or the restricted size Ramsey number for all pairs of graphs with at most four vertices and no isolated vertices is given.

ISSN:0364-9024    

DOI:10.1002/jgt.3190070107

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractThe (generalized) Ramsey numberr(G) is determined for all 113 graphs with no more than six lines and no isolated points. While few proofs are given, information is given which should be sufficient to reconstruct them in most cases.

ISSN:0364-9024    

DOI:10.1002/jgt.3190070108

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractChvátal established thatr(Tm, Kn) = (m– 1)(n– 1) + 1, whereTmis an arbitrary tree of ordermandKnis the complete graph of ordern. This result was extended by Chartrand, Gould, and Polimeni who showedKncould be replaced by a graph with clique numbernand ordern+ 1 providedn≧ 3 andm≧ 3. We further extend these results to show thatKncan be replaced by any graph onn+ 2 vertices with clique numbern, providedn≧ 5 andm≧ 4. We then show that further extensions, in particular to graphs onn+ 3 vertices with clique numbernare impossible. We also investigate the Ramsey number of trees versus complete graphs minus sets of independent edges. We show thatr(Tm, Kn–tK2) = (m– 1)(n – t– 1) + 1 form≧ 3,n≧ 6, whereTmis any tree of ordermexcept the star, and for

ISSN:0364-9024    

DOI:10.1002/jgt.3190070109

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractSuppose a graphGhas the property that if one colors the edges ofGinrcolors, there always exists a monochromatic triangle. Is it true that if one colors the edges ofGinr+ 1 colors so that every vertex is incident to at mostrcolors then there must be a monochromatic triangle? This problem, which was first raised by P. Erdös, is answered in the negative here

ISSN:0364-9024    

DOI:10.1002/jgt.3190070110

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY

摘要:

AbstractA pair of graphs (H1,H2) is a cleaver if there is a graphGwith a unique factorizationG = G2⊕G2such thatGidoes not contain a copy ofHi. (In caseH1=H2,H1is a cleaver if the factorization is unique up to interchange of factors.) A variety of positive and negative results on the existence of cleavers is obtained. For example (tree, complete graph) is a cleaver, and the triangle is the cleaver of an infinite collection of minimal graphs. On the other hand, stars are not cleaver

ISSN:0364-9024    

DOI:10.1002/jgt.3190070111

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1983

数据来源: WILEY