Operations preserving the pfaffian property of a graph

Operations preserving the pfaffian property of a graph
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DOI：
10.1017/s1446788700032730
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发表时间：
1991-04
期刊：
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
影响因子：
--
通讯作者：
C. Little;F. Rendl
C. Little;F. Rendl
中科院分区：
其他
文献类型：
--
作者：
C. Little;F. Rendl

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摘要根据Kasteleyn的规定，Pfaffian图是那些可以定向使1-因子具有等号的图。我们考虑了图上的各种运算，并考察了它们对Pfaffian性质的影响。我们证明了对Pfaffian图的研究可以归结为次三次图(没有顶点的度大于3的图)或Brick(3-连通双临界图)的情况。
Abstract Pfaffian graphs are those which can be oriented so that the 1-factors have equal sign, as calculated according to the prescription of Kasteleyn. We consider various operations on graphs and examine their effect on the Pfaffian property. We show that the study of Pfaffian graphs may be reduced to the case of subcubic graphs (graphs in which no vertex has degree greater than 3) or bricks (3-connected bicritical graphs).