Graphs and Combinatorics

, Volume 5, Issue 1, pp 189–196 | Cite as

Some extensions of a hypergraph

  • Sze-Chin Shee
Article
  • 35 Downloads

Abstract

It is shown how to construct a vertex-transitive hypergraphX* from a suitable collection of isomorphic copies of a given hypergraphX by identifying one or none of the vertices of every two copies in the collection. MoreoverX* andX have the same strong chromatic number.

If the hypergraphX is edge-coloured, thenX* can be so constructed that it is strongly vertex-colour-transitive. This paper also considers the case where a section hypergraph or none of the vertices of every two isomorphic copies is identified in the construction ofX*.

Keywords

Chromatic Number Isomorphic Copy Suitable Collection Strong Chromatic Number 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ang, S.L., Teh, H.H.: Finite homogeneous auto-extension of graphs, Nanta Math.1, 82–86 (1967)Google Scholar
  2. 2.
    Berge, C.: Graphs and Hypergraphs. Amsterdam: North-Holland Publishing Company 1973Google Scholar
  3. 3.
    Chen, C.C., Teh, H.H.: Construction of point-colour-symmetric graphs. J. Comb. Theory (B)27, 160–167 (1979)Google Scholar
  4. 4.
    Tan, K.W., Teh, H.H.: Finite auto-extension of graphs. Nanta Math.3, 33–41 (1969)Google Scholar
  5. 5.
    Teh, H.H.: Dimension and auto-extensions of graphs. Nanta Math.3, 23–32 (1969)Google Scholar
  6. 6.
    Teh, H.H., Shee, S.C.: Algebraic Theory of Graphs. Singapore: Lee Kong Chian Institute of Mathematics and Computer Science, Nanyang University, 1976Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Sze-Chin Shee
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingapore

Personalised recommendations