English

Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence

Combinatorics 2015-07-17 v1

Abstract

For a sequence dd of non-negative integers, let F(d){\cal F}(d) be the set of all forests whose degree sequence is dd. We present closed formulas for γmaxF(d)=max{γ(F):FF(d)}\gamma_{\max}^{\cal F}(d)=\max\{ \gamma(F):F\in {\cal F}(d)\} and αminF(d)=min{α(F):FF(d)}\alpha_{\min}^{\cal F}(d)=\min\{ \alpha(F):F\in {\cal F}(d)\} where γ(F)\gamma(F) and α(F)\alpha(F) are the domination number and the independence number of a forest FF, respectively.

Keywords

Cite

@article{arxiv.1507.04650,
  title  = {Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence},
  author = {Michael Gentner and Michael A. Henning and Dieter Rautenbach},
  journal= {arXiv preprint arXiv:1507.04650},
  year   = {2015}
}