Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

STRUCTURAL PROPERTIES FOR CERTAIN GLASSES OF INFINITE PLANAR GRAPHS

  • Published : 2003.09.01

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Abstract

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.

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References

  1. Canad. J. Math. v.18 Trees in polyhedral graphs D.W.Barnette
  2. J. Graph Th. v.23 Spanning paths in infinite planar graphs N.Dean;R.Thomas;X.Yu
  3. Graph Theory (2nd Ed.) R.Diestel
  4. Comm. Korean Math. Soc. v.11 On spanning 3-trees in infinite 3-connected planar graphs H.O.Jung
  5. J. Appl. Math. & Computing v.10 [2,3]=factors in a 3-connected infinite 3-connected infinite planar graphs H.O.Jung
  6. Unexplored and semi-explored territories in graph theory C.St.J.A.Nash-Williams;F.Harary(ed.)
  7. J. Graph Th. v.21 On Hamiltonian cycles in certain planar graphs D.P.Sanders
  8. J.Comb. Th. v.B no.62 4-connected projective planar graphs are Hamiltonian R.Thomas;X.Yu
  9. J. London Math. Soc. v.16 Straight line representations of infinite planar graphs C.Thomassen