Cubic graphs with equal independence number and matching number

Elena Mohr; Dieter Rautenbach

Cubic graphs with equal independence number and matching number

Combinatorics 2019-10-28 v1

Authors: Elena Mohr , Dieter Rautenbach

Abstract

Caro, Davila, and Pepper (arXiv:1909.09093) recently proved $\delta(G) \alpha(G)\leq \Delta(G) \mu(G)$ for every graph $G$ with minimum degree $\delta(G)$ , maximum degree $\Delta(G)$ , independence number $\alpha(G)$ , and matching number $\mu(G)$ . Answering some problems they posed, we characterize the extremal graphs for $\delta(G)<\Delta(G)$ as well as for $\delta(G)=\Delta(G)=3$ .

Keywords

graph theory graph theory of groups graph pebbling

Cite

@article{arxiv.1910.11762,
  title  = {Cubic graphs with equal independence number and matching number},
  author = {Elena Mohr and Dieter Rautenbach},
  journal= {arXiv preprint arXiv:1910.11762},
  year   = {2019}
}

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