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Almost Every Graph can be Covered by Linear Forests

Published online by Cambridge University Press:  12 September 2008

Colin McDiarmid  and
Bruce Reed
Colin McDiarmid
Affiliation:
Department of Statistics, Oxford University, Oxford, UK
Bruce Reed
Affiliation:
Institut für Diskrete Mathematik, University of Bonn, Germany
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Abstract

A linear forest is the union of a set of vertex disjoint paths. Akiyama, Exoo and Harary, and independently Hilton, have conjectured that the edges of every graph of maximum degree Δ can be covered by linear forests. We show that almost every graph can be covered with this number of linear forests.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 3 , September 1995 , pp. 257 - 268
Copyright
Copyright © Cambridge University Press 1995

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