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Graphs associated with triangulations of lattice polygons

Part of: Graph theory Real and complex geometry

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.
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Abstract

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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

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