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Triangular imbeddings into surfaces of a join of equicardinal independent sets following an Eulerian graph

Part of the Lecture Notes in Mathematics book series (LNM,volume 642)

Abstract

If G is a graph and m ≥ 1 an integer, G(m) is the graph obtained from G by replacing each vertex v by m vertices (v, 1), (v, 2), ..., (v, m) and joining two vertices (v, i) and (w, j) iff v and w are joined in G. G(m) is a particular case of a join in the sense of J. L. Jolivet [5]. Suppose that G has a triangular imbedding into a surface S (orientable or not); can we find a triangular imbedding of \(\overline G = G_{(m)}\)into a surface \(\overline S\)which has the same orientability characteristic as S? We give some sufficient conditions to have an affirmative answer to this question.

Keywords

  • Generative Chain
  • Local Orientation
  • Orientable Surface
  • Diagonal Component
  • Distinct Index

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1978 Springer-Verlag Berlin Heidelberg

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Bouchet, A. (1978). Triangular imbeddings into surfaces of a join of equicardinal independent sets following an Eulerian graph. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070367

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  • DOI: https://doi.org/10.1007/BFb0070367

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

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