Regular Graphs with Maximum Forest Number

  • Avapa Chantasartrassmee
  • Narong Punnim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


Punnim proved in [6] that if G is an r-regular graph of order n, then its forest number is at most c, where

$$c=\left\{ \begin{array} {ll} n-r+1 & {\rm if} \; r+1 \leq n \leq 2r-1,\\ \lfloor \frac{nr-2}{2(r-1)} \rfloor & {\rm if}\; n\geq 2r. \end{array} \right.$$

He also proved that the bound is sharp. Let \({\cal{R}}(r^{n};c)\) be the class of all r-regular graphs of order n. We prove in this paper that if \(G, H\in{\cal{R}}(r^{n};c)\), then there exists a sequence of switchings σ 1, σ 2, …, σ t such that for each i = 1, 2, …, t, \(G^{\sigma_1\sigma_2\cdots\sigma_i}\in{\cal{R}}(r^n;c)\) and \(H=G^{\sigma_1\sigma_2\cdots\sigma_t}\).


Planar Graph Nonnegative Integer Regular Graph Degree Sequence Graphical Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Avapa Chantasartrassmee
    • 1
  • Narong Punnim
    • 2
  1. 1.University of the Thai Chamber of CommerceBangkokThailand
  2. 2.Srinakharinwirot UniversityBangkok

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