Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T14:11:38.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Graphs associated with triangulations of lattice polygons

Part of: Real and complex geometry Graph theory

Published online by Cambridge University Press:  09 April 2009

Duane DeTemple  and
Jack M. Robertson
Duane DeTemple
Affiliation:
Department of Pure and Applied Mathematics, Washington State University Pullman, Washington 99164–2930, U.S.A.
Jack M. Robertson
Affiliation:
Department of Pure and Applied Mathematics, Washington State University Pullman, Washington 99164–2930, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two graphs, the edge crossing graph E and the triangle graph T are associated with a simple lattice polygon. The maximal independent sets of vertices of E and T are derived including a formula for the size of the fundamental triangles. Properties of E and T are derived including a formula for the size of the maximal independent sets in E and T. It is shown that T is a factor graph of edge-disjoint 4-cycles, which gives corresponding geometric information, and is a partition graph as recently defined by the authors and F. Harary.

MSC classification

Secondary: 05C99: None of the above, but in this section 51M05: Euclidean geometries (general) and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 391 - 398
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Coxeter, H. S. M., Introduction to geometry, (Wiley, New York, 1961).Google Scholar
[2]DeTemple, D., Harary, F. and Robertson, J., ‘Partition graphs’, Soochow J. Math. 13 (1987), 121–129.Google Scholar
[3]DeTemple, D., Harary, F. and Roberston, J., ‘Existential partition graphs’, J. Combin. Inform. Systems Sci. 9 (1984), 193–196.Google Scholar
[4]DeTemple, D. and Robertson, J., ‘Constructions and the realization problem for partition graphs’, J. Combin. Inform. Systems Sci. (to appear).Google Scholar
[5]Garey, M. and Johnson, D., Computer and intractibility: a guide to the theory of NP-completeness, (Freeman, San Francisco, 1979).Google Scholar
[6]Gavril, F., ‘Some NP-complete problems on graphs’, Proc. 11th Conf. Inf. Sci. Systems, (John Hopkins University, Baltimore, 1977, 91–95).Google Scholar
[7]Harary, F., Graph theory, (Addison-Wesley, Reading, 1969).CrossRefGoogle Scholar
[8]Valiant, L., ‘The complexity of enumeration and reliability problems’, SIAM J. Comput. 8 (1979), 410–421.Google Scholar