Skip to Main content Skip to Navigation
Conference papers

The analysis of a prioritised probabilistic algorithm to find large induced forests in regular graphs with large girth

Abstract : The analysis of probabilistic algorithms has proved to be very successful for finding asymptotic bounds on parameters of random regular graphs. In this paper, we show that similar ideas may be used to obtain deterministic bounds for one such parameter in the case of regular graphs with large girth. More precisely, we address the problem of finding a large induced forest in a graph $G$, by which we mean an acyclic induced subgraph of $G$ with a lot of vertices. For a fixed integer $r \geq 3$, we obtain new lower bounds on the size of a maximum induced forest in graphs with maximum degree $r$ and large girth. These bounds are derived from the solution of a system of differential equations that arises naturally in the analysis of an iterative probabilistic procedure to generate an induced forest in a graph. Numerical approximations suggest that these bounds improve substantially the best previous bounds. Moreover, they improve previous asymptotic lower bounds on the size of a maximum induced forest in a random regular graph.
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185567
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 4:32:07 PM
Last modification on : Tuesday, March 7, 2017 - 3:07:03 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:48:19 AM

File

dmAM0126.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185567, version 1

Collections

Citation

Carlos Hoppen. The analysis of a prioritised probabilistic algorithm to find large induced forests in regular graphs with large girth. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.373-386. ⟨hal-01185567⟩

Share

Metrics

Record views

87

Files downloads

595