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Inequalities involving the genus of a graph and its thicknesses†

Published online by Cambridge University Press:  18 May 2009

Lowell W. Beineke  and
Frank Harary
Lowell W. Beineke
Affiliation:
University of Michigan Ann Arbor, Michigan, U.S.A.
Frank Harary
Affiliation:
University of Michigan Ann Arbor, Michigan, U.S.A.
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Let G be a graph with p points and q lines, and genus γ. The thicknesst(G) has been introduced as the minimum number of planar subgraphs whose union is G. This topological invariant of a graph has been studied by Battle, Harary and Kodama [1], Tutte [7], Beineke, Harary and Moon [3], and Beineke and Harary [2].

It is natural to generalise this concept of the thickness of a graph to the union of graphs with a specified genus. We say that the n-thickness of G is the minimum number of subgraphs of genus at most n whose union is G. Denoting the n-thickness of G by tn, we write in particular t0 the 0-thickness, i.e., the thickness.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 1 , January 1965 , pp. 19 - 21
Copyright
Copyright © Glasgow Mathematical Journal Trust 1965

References

REFERENCES

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