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A combinatorial proof of a theorem of Tutte‡

Published online by Cambridge University Press:  24 October 2008

John H. Halton
John H. Halton
Affiliation:
Applied Mathematics Department, Brookhaven National Laboratory, Upton, Long Island, New York§
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Extract

We refer to a beautiful and important result of Tutte(1), in the theory of graphs; that a linear graph G is prime if and only if it contains a set ∑ of vertices, such that u(G∑) > n(∑); where n(∑) is the number of vertices in ∑, G∑ is the graph obtained from G by deleting the star of ∑ (all the vertices of G in ∑, together with all the edges of G meeting vertices of ∑), and u(G∑) is the number of connected components of G∑ having an odd number of vertices.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 683 - 684
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Tutte, W. T.The factorization of linear graphs. J. London Math. Soc. 22 (1947), 107–111.CrossRefGoogle Scholar
(2)Maunsell, F. G.A note on Tutte's paper ‘The factorization of linear graphs’. J. London Math. Soc. 27 (1952), 127–128.CrossRefGoogle Scholar