Sharp upper bounds on the $k$-independence number in graphs with given minimum and maximum degree

Zhenyu Taoqiu; Suil O; Yongtang Shi

Sharp upper bounds on the $k$-independence number in graphs with given minimum and maximum degree

Combinatorics 2020-09-01 v3

Authors: Zhenyu Taoqiu , Suil O , Yongtang Shi

Abstract

The $k$ -independence number of a graph $G$ is the maximum size of a set of vertices at pairwise distance greater than $k$ . In this paper, for each positive integer $k$ , we prove sharp upper bounds for the $k$ -independence number in an $n$ -vertex connected graph with given minimum and maximum degree.

Keywords

graph pebbling graph theory graph connectivity

Cite

@article{arxiv.1901.06607,
  title  = {Sharp upper bounds on the $k$-independence number in graphs with given minimum and maximum degree},
  author = {Zhenyu Taoqiu and Suil O and Yongtang Shi},
  journal= {arXiv preprint arXiv:1901.06607},
  year   = {2020}
}

Comments

16 pages, 11 figures

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