Necessary and sufficient conditions for a graph to be three-terminal series-parallel-cascade

نویسندگان

  • Takao Nishizeki
  • Nobuji Saito
چکیده

A “three-terminal series-parallel-cascade graph” is defined as a three-terminal* graph which is constructed by means of cascade connections in addition to series and parallel connections which were used in constructing a three-terminal series-parallel graph in our previous paper. Some properties of the graph are presented, and a theorem of the Kuratowski type is given stating that a threeterminal nonseparable graph is three-terminal series-parallel-cascade if and only if none of certain three graphs can be obtained from it by opening or shorting some of the edges. This theorem characterizes a three-terminal series-parallelcascade graph completely, and clarifies its structual limitation.

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عنوان ژورنال:
  • J. Comb. Theory, Ser. B

دوره 24  شماره 

صفحات  -

تاریخ انتشار 1978