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PM-compact Graphs and Vertex-deleted Subgraphs

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Abstract

The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings of G. A graph G is PM-compact if the 1-skeleton graph of the prefect matching polytope of G is complete. Equivalently, a matchable graph G is PM-compact if and only if for each even cycle C of G, G ∔ V(C) has at most one perfect matching. This paper considers the class of graphs from which deleting any two adjacent vertices or nonadjacent vertices, respectively, the resulting graph has a unique perfect matching. The PM-compact graphs in this class of graphs are presented.

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Acknowledgments

The authors would like to thank the Associate Editor (AE) and two anonymous referees for their helpful comments on improving the representation of the paper.

Funding

This paper is supported by the National Natural Science Foundation of China (Nos. 12171440, 11971445).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Yi-pei Zhang, Xiu-mei Wang & Jin-jiang Yuan

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  1. Yi-pei Zhang
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  2. Xiu-mei Wang
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  3. Jin-jiang Yuan
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Correspondence to Xiu-mei Wang.

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Zhang, Yp., Wang, Xm. & Yuan, Jj. PM-compact Graphs and Vertex-deleted Subgraphs. Acta Math. Appl. Sin. Engl. Ser. 38, 955–965 (2022). https://doi.org/10.1007/s10255-022-1018-3

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  • DOI: https://doi.org/10.1007/s10255-022-1018-3

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