摘要:

AbstractThe main subjects of this survey paper are Hamitonian cycles, cycles of prescirbed lengths, cycles in tournaments, and partitions, packings, and coverings by cycles. Several unsolved problems and a bibiligraphy are included.

ISSN:0364-9024    

DOI:10.1002/jgt.3190050102

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

年代:1981

数据来源: WILEY

摘要:

AbstractVizing's Theorem states that any graphGhas chromatic index either the maximum degree Δ(G) or Δ(G) + 1. IfGhas 2s+ 1 points and Δ(G) = 2s, a well‐known necessary condition for the chromatic index to equal 2sis thatGhave at most 2s2lines. Hilton conjectured that this condition is also sufficient. We present a proof of that conjecture and a corollary that helps determine the chromatic index of some graphs with 2s points and maximum degree 2s

ISSN:0364-9024    

DOI:10.1002/jgt.3190050103

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

年代:1981

数据来源: WILEY

摘要:

AbstractA generalized type of graph covering, called a “Wrapped quasicovering” (wqc) is defined. IfK, Lare graphs dually embedded in an orientable surfaceS, then we may lift these embeddings to embeddings of dual graphs K̃,L̃ in orientable surfaces S̃, such that S̃ are branched covers ofSand the restrictions of the branched coverings to K̃,L̃ are wqc's ofK, L.the theory is applied to obtain genus embeddings of composition graphsG[nK1] from embeddings of “quotie

ISSN:0364-9024    

DOI:10.1002/jgt.3190050104

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

年代:1981

数据来源: WILEY

摘要:

AbstractWith the aid of a computer. we give a regular graph of girth 6 and valency 7, which has 90 vertices and show that this is the unique smallest graph with these properties.

ISSN:0364-9024    

DOI:10.1002/jgt.3190050105

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

年代:1981

数据来源: WILEY

摘要:

AbstractThe graph of O'Keefe and Wong, with valency 7, girth 6, and 90 vertices, is constructed as a 3‐fold covering graph, and it is shown that there is a unique covering graph with these propertie

ISSN:0364-9024    

DOI:10.1002/jgt.3190050106

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

年代:1981

数据来源: WILEY

摘要:

AbstractA graphGis called the 2‐amalgamationof subgraphsG1andG2ifG=G1∪G2andG1∩G2= {x, y}, 2 distinct points. in this case we writeG=G1∪{x, y}G2. in this paper we show that the orientable genus, γ(G), satisfies the inequalities γ(G1) + γ(G2) − 1 ≤ γ(G1∪{x, y}G2) ≤ γ(G1) + γ(G2) + 1 and that this is the best possible result, i. e., the resulting three values for γ(G1∪{x, y}G2) which are possible can actually be realized by approp

ISSN:0364-9024    

DOI:10.1002/jgt.3190050107

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

年代:1981

数据来源: WILEY

摘要:

AbstractIn this series, we investigate the conditions under which both a graphGand its complementGpossess certain specified properties. We now characterize all the graphsGsuch that bothGandGhave the same number of endpoints, and find that this number can only be 0 or 1 or 2. As a consequence, we are able to enumerate the self‐complementary block

ISSN:0364-9024    

DOI:10.1002/jgt.3190050108

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

年代:1981

数据来源: WILEY

摘要:

AbstractLetr(k) denote the least integern‐such that for any graphGonnvertices eitherGor its complementGcontains a complete graphKkonkvertices. in this paper, we prove the following lower bound for the Ramsey numberr(k) by explicit construction:r(k) ≥ exp (c(Logk)4/3[(log logk)1/3] for some constant

ISSN:0364-9024    

DOI:10.1002/jgt.3190050109

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

年代:1981

数据来源: WILEY

ISSN:0364-9024    

DOI:10.1002/jgt.3190050110

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

年代:1981

数据来源: WILEY

ISSN:0364-9024    

DOI:10.1002/jgt.3190050101

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

年代:1981

数据来源: WILEY