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Induced Forests in Regular Graphs with Large Girth

Published online by Cambridge University Press:  01 May 2008

CARLOS HOPPEN  and
NICHOLAS WORMALD
CARLOS HOPPEN
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, CanadaN2L 3G1 (e-mail: choppen@math.uwaterloo.ca, nwormald@uwaterloo.ca)
NICHOLAS WORMALD
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, CanadaN2L 3G1 (e-mail: choppen@math.uwaterloo.ca, nwormald@uwaterloo.ca)
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Abstract

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An induced forest of a graph G is an acyclic induced subgraph of G. The present paper is devoted to the analysis of a simple randomized algorithm that grows an induced forest in a regular graph. The expected size of the forest it outputs provides a lower bound on the maximum number of vertices in an induced forest of G. When the girth is large and the degree is at least 4, our bound coincides with the best bound known to hold asymptotically almost surely for random regular graphs. This results in an alternative proof for the random case.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 389 - 410
Copyright
Copyright © Cambridge University Press 2008

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