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ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory  18(1) (1998)   113-125
DOI: 10.7151/dmgt.1068


Izak Broere

Michael Dorfling

Rand Afrikaans University
Auckland Park, 2006 South Africa

Jean E. Dunbar

Converse College
Spartanburg, SC 29302 USA

Marietjie Frick

University of South Africa
Pretoria, 0001 South Africa


Let τ(G) denote the number of vertices in a longest path of the graph G and let k1 and k2 be positive integers such that τ(G) = k1 +k2. The question at hand is whether the vertex set V(G) can be partitioned into two subsets V1 and V2 such that τ(G[V1] ) ≤ k1 and τ(G[ V2] ) ≤ k2. We show that several classes of graphs have this partition property.

Keywords: vertex partition, τ-partitionable, decomposable graph.

1991 Mathematics Subject Classification: 05C38.


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Received 10 October 1997
Revised 27 February 1998