Induced forests in regular graphs with large girth

Authors:
Carlos Hoppen;Nicholas Wormald
Affiliations:
Department of combinatorics and optimization, university of waterloo, waterloo on, canadan2l 3g1 (e-mail: choppen@math.uwaterloo.ca, nwormald@uwaterloo.ca);Department of combinatorics and optimization, university of waterloo, waterloo on, canadan2l 3g1 (e-mail: choppen@math.uwaterloo.ca, nwormald@uwaterloo.ca)
Venue:
Combinatorics, Probability and Computing
Year:
2008

Citing 7
Cited 2

Maximum induced trees in graphs

Journal of Combinatorial Theory Series B
On the feedback vertex set problem in permutation graphs

Information Processing Letters
Decycling graphs

Journal of Graph Theory
Fragmentability of graphs

Journal of Combinatorial Theory Series B
Decycling numbers of random regular graphs

Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
On the Independent Domination Number of Random Regular Graphs

Combinatorics, Probability and Computing
Large independent sets in regular graphs of large girth

Journal of Combinatorial Theory Series B

Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs

Random Structures & Algorithms
Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.