Decycling numbers of random regular graphs

: 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.

• Type: Journal
• Year: 2002
• Where: RSA
• Authors: Sheng Bau, Nicholas C. Wormald, Sanming Zhou
• Keywords: Decycling Numbers, Random Cubic Graph, Random Regular Graphs, RSA 2002