SIAM Journal on Discrete Mathematics


SIAM J. Discrete Math., 25(4), 1804–1811. (8 pages)

Covering a Graph by Forests and a Matching

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Article Data

History

Submitted: 15 December 2010
Accepted: 09 September 2011
Published online: 15 December 2011

AMS Subject Headings

05C70

Publication Data

ISSN (print): 0895-4801
ISSN (online): 1095-7146
Publisher: Society for Industrial and Applied Mathematics
CODEN: sjdmec
Tomáš Kaiser, Mickaël Montassier, and André Raspaud
https://doi.org/10.1137/100818340

We prove that for any positive integer k, the edges of any graph whose fractional arboricity is at most $k + 1/(3k+2)$ can be decomposed into k forests and a matching. This is a partial result in the direction of the “Nine Dragon Tree” conjecture of Montassier et al.

Copyright © 2011 Society for Industrial and Applied Mathematics
Permalink: https://doi.org/10.1137/100818340

Cited by

(2019) Decomposing 4-connected planar triangulations into two trees and one path. Journal of Combinatorial Theory, Series B 134, 88-109. Crossref
(2018) Decomposing a graph into forests and a matching. Journal of Combinatorial Theory, Series B 131, 40-54. Crossref