ISSN:0364-9024    

DOI:10.1002/jgt.3190050302

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.3190050303

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

年代:1981

数据来源: WILEY

摘要:

AbstractWe present three short proofs of Kuratowski's theorem on planarity of graphs and discuss applications, extensions, and some related problems.

ISSN:0364-9024    

DOI:10.1002/jgt.3190050304

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.3190050305

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

年代:1981

数据来源: WILEY

摘要:

AbstractSome classes of graphs are described which are extensions of bipartite multigraphs. Exclusion of some specific partial subgraphs gives some properties of edge colorability. in particular sufficient conditions are developed for the existence of generalized good and equitable colorings.

ISSN:0364-9024    

DOI:10.1002/jgt.3190050306

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

年代:1981

数据来源: WILEY

摘要:

AbstractDirect proofs of some planarity criteria are presented.

ISSN:0364-9024    

DOI:10.1002/jgt.3190050307

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

年代:1981

数据来源: WILEY

摘要:

AbstractA (plane) 4‐regular mapGis calledC‐simple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case σ (G) is the smallest integerksuch that the curves ofGcan be colored withkcolors in such a way that no two curves of the same color intersect. We prove that if σ (G) ≤ 4,Gis edge colorable with 4 colors. Moreover we show that a similar result for mapsGwith σ(G) ≤ 5 would imply the Four‐C

ISSN:0364-9024    

DOI:10.1002/jgt.3190050308

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

年代:1981

数据来源: WILEY

摘要:

AbstractLetE1……Embe the edges of a hypergraph. Assume each element in the union of the edges occurs in at least two ofE1……Em. Assume further that every pair of distinct edges,E1, andE1, intersect in at most one element and that for each such pair there are exactly λ other edgesEksuch thatE1andE1both intersectEk. We characterize the hypergraphs for which each |E1| ≤ 2. These are the λ‐complet

ISSN:0364-9024    

DOI:10.1002/jgt.3190050309

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

年代:1981

数据来源: WILEY

摘要:

AbstractThe matching polynomial α(G, x) of a graphGis a form of the generating function for the number of sets ofkindependent edges ofG. in this paper we show that ifGis a graph with vertexvthen there is a treeTwith vertexwsuch that\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\alpha (G\backslash v, x)}}{{\alpha (G, x)}} = \frac{{\alpha (T\backslash w, x)}}{{\alpha (T, x)}}. $\end{document}This result has a number of consequences. Here we use it to prove that α(G\v, 1/x)/xα(G, 1/x) is the generating function for a certain class of walks inG.As an application of these results we then establish some new properties of α(G,

ISSN:0364-9024    

DOI:10.1002/jgt.3190050310

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

年代:1981

数据来源: WILEY

摘要:

AbstractBurr recently proved [3] that for positive integersm1,m2……mk, and any graphGwe haveX(G)\documentclass{article}\pagestyle{empty}\begin{document}$ \chi (G)\, \le \,\mathop \prod \limits_{i = 1}^k m_i $\end{document}if and only ifGcan be expressed as the edge disjoint union of subgraphsFisatisfyingX(Fi) ≤mi. This theorem is generalized to hypergraphs. By suitable interpretations the generalization is then used to deduce propositions on coverings of g

ISSN:0364-9024    

DOI:10.1002/jgt.3190050311

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

年代:1981

数据来源: WILEY