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RSA

2002

2002

: The decycling number (G) of a graph G is the smallest number of vertices which can be removed from G so that the resultant graph contains no cycles. In this paper, we study the decycling numbers of random regular graphs. For a random cubic graph G of order n, we prove that (G) n/4 1/2 holds asymptotically almost surely. This is the result of executing a greedy algorithm for decycling G making use of a randomly chosen Hamilton cycle. For a general random d-regular graph G of order n, where d 4, we prove that (G)/n can be bounded below and above asymptotically almost surely by certain constants b(d) and B(d), depending solely on d, which are determined by solving, respectively, an algebraic equation and a system of differential equations.

Related Content

Added |
23 Dec 2010 |

Updated |
23 Dec 2010 |

Type |
Journal |

Year |
2002 |

Where |
RSA |

Authors |
Sheng Bau, Nicholas C. Wormald, Sanming Zhou |

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