摘要:

AbstractIn this note a shortened proof is given for the Faudree—Schelp theorem on path‐connected gra

ISSN:0364-9024    

DOI:10.1002/jgt.3190080112

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

年代:1984

数据来源: WILEY

摘要:

AbstractAgraphLis called a link graph if there is a graphGsuch that for each vertex ofGits neighbors induce a subgraph isomorphic toL.Such a G is said to have constant link.L Sabidussi proved that for any finite group F and anyn⩾ 3 there are infinitely manyn‐regular connected graphsGwith AutG≅ Γ. We will prove a stronger result: For any finite group Γ and any link graphLwith at least one isolated vertex and at least three vertices there are infinitely many connected graphsGwith constant linkLand

ISSN:0364-9024    

DOI:10.1002/jgt.3190080113

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

年代:1984

数据来源: WILEY

摘要:

AbstractIt is shown using enumeration results that forr>2t, almost all labeledr‐regular graphs cannot be factorized intot⩾ 2 isomorphic subgraphs. However, no examples of such nonfactorizable graphs are known which satisfy the obvious divisibility condition that the number of edges is divisible byt.Similar observations hold for regular tournaments (t⩾ 2} and forr‐regular digraphs (

ISSN:0364-9024    

DOI:10.1002/jgt.3190080114

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

年代:1984

数据来源: WILEY

摘要:

AbstractNew upper and lower bounds for the chromatic index of a finite muitigraph are obtained. A complete description is given of multigraphs satisfying χ′>1/8(9ρ + 6) where χ′ and ρ denote the chromatic index and the maximum vertex degree of a multigraph. Some new and old conjectures are di

ISSN:0364-9024    

DOI:10.1002/jgt.3190080115

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

年代:1984

数据来源: WILEY

摘要:

AbstractThere have been a number of results dealing with Hamiltonian properties in powers of graphs. In this paper we show that the square and the total graph of aK1,3‐free graph are vertex pancyclic. We then discuss some of the relationships between connectivity and Hamiltonian properties inK1,3‐free gra

ISSN:0364-9024    

DOI:10.1002/jgt.3190080116

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

年代:1984

数据来源: WILEY

摘要:

AbstractVarious Harniltonian‐like properties are investigated in the squares of connected graphs free of some set of forbidden subgraphs. The starK1,4the subdivision graph ofK1,3, and the subdivision graph ofK1,3minus an endvertex play central roles. In particular, we show that connected graphs free of the subdivision graph ofK1,3minus an endvertex have vertex pancyclic square

ISSN:0364-9024    

DOI:10.1002/jgt.3190080117

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

年代:1984

数据来源: WILEY

摘要:

AbstractWe consider two new classes of graphs arising from reliability considerations in network design. We want to construct graphs with a minimum number of edges which remain Hamiltonian afterkedges (orkvertices) have been removed. A simple construction is presented for the case whenkis even. We show that it is minimumk‐edge Hamiltonian. On the other hand, Chartrand and Kapoor previously proved that this class of graphs was also minimumk‐vertex Hamiltonian. The case whenkis large (odd or even) is also considered. Some results about directed graphs are also presen

ISSN:0364-9024    

DOI:10.1002/jgt.3190080118

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

年代:1984

数据来源: WILEY

摘要:

AbstractThis note can be treated as a supplement to a paper written by Bollobas which was devoted to the vertices of a given degree in a random graph. We determine some values of the edge probabilitypfor which the number of vertices of a given degree of a random graphG∈

ISSN:0364-9024    

DOI:10.1002/jgt.3190080119

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

年代:1984

数据来源: WILEY

摘要:

AbstractIn this note the second moment of the vertex degree sequence of planar graphs is considered. We prove that1IfGis an outerplanar graph of ordern⩾ 3 then2IfGis a planar graph of ordern⩾ 4 thenwhered1,…,dnis the vertex degree sequence ofG.We exhibit all graphs for which these upper bounds are att

ISSN:0364-9024    

DOI:10.1002/jgt.3190080120

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

年代:1984

数据来源: WILEY

摘要:

AbstractThe Ramsey numbersr(Kp,n1P2,…,ndP2),p>2, are calculate

ISSN:0364-9024    

DOI:10.1002/jgt.3190080121

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

年代:1984

数据来源: WILEY