• Title/Summary/Keyword: semicycle structures

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STRUCTURAL PROPERTIES FOR CERTAIN GLASSES OF INFINITE PLANAR GRAPHS

  • Jung, Hwan-Ok
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.105-115
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    • 2003
  • An infinite locally finite plane graph is called an LV-graph if it is 3-connected and VAP-free. If an LV-graph G contains no unbounded faces, then we say that G is a 3LV-graph. In this paper, a structure theorem for an LV-graph concerning the existence of a sequence of systems of paths exhausting the whole graph is presented. Combining this theorem with the early result of the author, we obtain a necessary and sufficient conditions for an infinite VAP-free planar graph to be a 3LV-graph as well as an LV-graph. These theorems generalize the characterization theorem of Thomassen for infinite triangulations.