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.
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This Work is Supported by Hanshin University Research Grants 2003.
Hwan-Ok Jung received his BS degree from Seoul National University, Korea, and MS and Ph. D. from Universitat Hamburg, Germany, under the direction of Prof. Dr. R. Halin. Since 1989 he has been a full professor of Hanshin University. His research interests: hamiltonian paths, spanning trees and factors in infinite graphs.
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Jung, H. Structural properties for certain classes of infinite planar graphs. JAMC 13, 105 (2003). https://doi.org/10.1007/BF02936078
AMS Mathematics Subject Classification
Key words and phrases
- semicycle structures
- planar graphs
- structural characterizations
- infinite graphs