Structural properties for certain classes of infinite planar graphs

  • Hwan-Ok Jung


An infinite locally finite plane graph is called an LV-graph if it is 3-connected and VAP-free. If an LV-graphG contains no unbounded faces, then we say thatG 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.

AMS Mathematics Subject Classification

05C10 05C75 

Key words and phrases

semicycle structures planar graphs structural characterizations infinite graphs 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2003

Authors and Affiliations

  1. 1.Departent of MathematicsHanshin UniversityOsanKorea

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