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Path decompositions of digraphs

Published online by Cambridge University Press:  17 April 2009

Issam Abdul-Kader
Issam Abdul-Kader
Affiliation:
Faculty of Science, Lebanese University, Beirut, Lebanon.
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Abstract

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Let G = (X, U) be a digraph of order n. P(G) denotes the minimal cardinal of a path-partition of the arcs of G.

Oystein Ore, Theory of graphs (Amer. Math. Soc, Providence, Rhode Island, 1962) has proved that , where . We say that G satisfies Q if the preceeding inequality is an equality.

We give some properties of the digraphs satisfying Q, and in particular the case where G is strongly connected. Then we prove that P(G) ≤ [n2/4], and that this result is the best possible. Next we exhibit the existence of digraphs with circuits such that P(G) = [n2/4].

Finally we prove that if G is a strongly connected digraph of order n which satisfies Q, then there exists a strongly connected digraph H of order n + 1 having G as a sub-digraph and satisfying Q, too.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 2 , October 1978 , pp. 205 - 216
Copyright
Copyright © Australian Mathematical Society 1979

References

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