摘要:

AbstractWe find all possible lengths of circuits in Cayley digraphs of two‐generated abelian groups over the two‐element generating sets and over certain three‐element generating

ISSN:0364-9024    

DOI:10.1002/jgt.3190140112

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

年代:1990

数据来源: WILEY

摘要:

AbstractThe vertexlineararboricity vla(G) of a nonempty graphGis the minimum number of subsets into which the vertex setV(G)can be partitioned so that each subset induces a subgraph whose connected components are paths. This paper provides an upper bound for vla(G) of a connected nonempty graphG, namely vla(G) ≦ 1 + ⌊δ(G)/2⌋ where δ(G) denotes the maximum degree ofG. Moreover, if δ(G) is even, then vla(G) = 1 + ⌊δ(G)/2⌋ if and only ifGis either a cycle or a c

ISSN:0364-9024    

DOI:10.1002/jgt.3190140113

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

年代:1990

数据来源: WILEY

摘要:

AbstractLetMbe a matching in a graphGsuch thatd(x) +d(y) ≥ |G| for all pairs of independent vertices x and y of G that are incident withM.We determine a necessary and sufficient condition forMto be contained in a cycle ofG.This extends results of Häggkvist and Berman, and implies that ifMis a 1‐factor ofGand |G|  0 (mod 4), thenMis contained in a Hamilton cycle ofG. We use our results to deduce that an eulerian graph of minimum degree 2k contains k pairwise compatible Euler

ISSN:0364-9024    

DOI:10.1002/jgt.3190140114

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

年代:1990

数据来源: WILEY

ISSN:0364-9024    

DOI:10.1002/jgt.3190140115

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

年代:1990

数据来源: WILEY

ISSN:0364-9024    

DOI:10.1002/jgt.3190140101

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

年代:1990

数据来源: WILEY