Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A STRUCTURE THEOREM AND A CLASSIFICATION OF AN INFINITE LOCALLY FINITE PLANAR GRAPH

  • 발행 : 2009.05.31
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초록

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

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참고문헌

  1. M. Chastand and N. Polat, Reconstruction of infinite locally finite connected graphs, Disc. Math. 270 (2003), 61–98. https://doi.org/10.1016/S0012-365X(02)00867-1
  2. R. Diestel, Graph Theory (3nd Ed.), Springer-Verlag, Heidelberg, 2005.
  3. R. Diestel and P. Sprussel, The homology of locally finite graphs with ends, to appear.
  4. R. Halin, Uber unendliche Wege in Graphen, Math. Ann. 157 (1964), 125–137. https://doi.org/10.1007/BF01362670
  5. H. Jung, Wurzelbaume und unendliche Wege in Graphen, Math. Nachr. 41 (1969), 1–22. https://doi.org/10.1002/mana.19690410102
  6. H. Jung, Structural properties for certain classes of infinite planar graphs, J. Appl. Math.& computing 13 (2004), 105–115.
  7. H. Jung, An extension of Salle's theorem to infinite locally finite VAP-free plane graphs,J. Appl. Math. & computing 22 (2006), 83–93. https://doi.org/10.1007/BF02896462
  8. C. Thomassen, Planarity and duality of finite and infinite graphs, J. Comb. Th. (B) 29 (1980), 244–271.