ISSN:0364-9024    

DOI:10.1002/jgt.3190070402

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.3190070403

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

年代:1983

数据来源: WILEY

摘要:

AbstractThe Ramsey numberr(G, H)is evaluated exactly in certain cases in which bothGandHare complete multipartite graphsK(n,1, n2, …. nk). Specifically, each of the following cases is handled whenevernis sufficiently large:r(K(1, m1, …. mk), K(1, n)), r(K(1, m), K(n1, …. nk, n)), providedm ≧ 4, and r(K(1, 1, m), K(nk, …

ISSN:0364-9024    

DOI:10.1002/jgt.3190070404

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

年代:1983

数据来源: WILEY

摘要:

AbstractA graph is locally connected if for each vertex ν of degree≧2, the subgraph induced by the vertices adjacent to ν is connected. In this paper we establish a sharp threshold function for local connectivity. Specifically, if the probability of an edge of a labeled graph of ordernisp= ((3/2 +ϵn)logn/n)1/2whereϵn= (log logn+ log(3/8) + 2x)/(2 logn), then the limiting probability that a random graph is locally connected is exp(‐e

ISSN:0364-9024    

DOI:10.1002/jgt.3190070405

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

年代:1983

数据来源: WILEY

摘要:

AbstractThe Hamiltonian path graphH(G)of a graphGis that graph having the same vertex set asGand in which two verticesuandvare adjacent if and only ifGcontains a Hamiltonianu‐vpath. A characterization of Hamiltonian graphs isomorphic to their Hamiltonian path graphs is presente

ISSN:0364-9024    

DOI:10.1002/jgt.3190070406

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

年代:1983

数据来源: WILEY

摘要:

AbstractIn this paper it is shown that anym‐regular graph of order 2m(m ≧ 3), not isomorphic toKm,m, or of order 2m+ 1 (meven,m ≧4), is Hamiltonian connected, which extends a previous result of Nash‐Williams. As a corollary, it is derived that any such graph contains atleastmHamiltonian cycles for oddmand atleast 1/2mHamiltonian cycles fo

ISSN:0364-9024    

DOI:10.1002/jgt.3190070407

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

年代:1983

数据来源: WILEY

摘要:

AbstractBased on the terms “end” and “cofinal spanning subtree” a general notion of Hamiltonicity of infinite graphs is developed. It is shown that the cube of every connected locally finite graph is Hamiltonian in this generalize

ISSN:0364-9024    

DOI:10.1002/jgt.3190070408

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

年代:1983

数据来源: WILEY

摘要:

AbstractWe show that the Cartesian productZa× Zbof two directed cycles is hypo‐Hamiltonian (Hamiltonian) if and only if there is a pair of relatively prime positive integersmandnwithma+nb=ab‐ 1 (ma+nb=ab). The result for hypo‐Hamiltonian is new; that for Hamiltonian is known. These are special cases of the fact that there is a simple circuit of lengthpinZa× Zbif and only if there is a pair of relatively prime non‐negative integersmandnwithm

ISSN:0364-9024    

DOI:10.1002/jgt.3190070409

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

年代:1983

数据来源: WILEY

摘要:

AbstractThe main purpose of this paper is to show that any embedding ofK7in three‐dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding ofK6contains a pair of disjoint cycles which are homologically linke

ISSN:0364-9024    

DOI:10.1002/jgt.3190070410

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

年代:1983

数据来源: WILEY

摘要:

AbstractWe show the uniqueness of the strongly regular graph with parametersν = 77, k = 16, λ = O, μ = 4embedding it in the Higman‐Sims graph as a second subconstituent, and indicate the existence of a sporadic geom

ISSN:0364-9024    

DOI:10.1002/jgt.3190070411

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

年代:1983

数据来源: WILEY