# Construction and characterization of graphs whose each spanning tree has a perfect matching

@article{Wu2016ConstructionAC, title={Construction and characterization of graphs whose each spanning tree has a perfect matching}, author={Baoyindureng Wu and Heping Zhang}, journal={arXiv: Combinatorics}, year={2016} }

An edge subset $S$ of a connected graph $G$ is called an anti-Kekul\'{e} set if $G-S$ is connected and has no perfect matching. We can see that a connected graph $G$ has no anti-Kekul\'{e} set if and only if each spanning tree of $G$ has a perfect matching. In this paper, by applying Tutte's 1-factor theorem and structure of minimally 2-connected graphs, we characterize all graphs whose each spanning tree has a perfect matching In addition, we show that if $G$ is a connected graph of order $2n…

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