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Fractional matching preclusion of graphs

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Abstract

Let F be an edge subset and \(F^{\prime }\) a subset of edges and vertices of a graph G. If \(G-F\) and \(G-F^{\prime }\) have no fractional perfect matchings, then F is a fractional matching preclusion (FMP) set and \(F^{\prime }\) is a fractional strong MP (FSMP) set of G. The FMP (FSMP) number of G is the minimum size of FMP (FSMP) sets of G. In this paper, the FMP number and the FSMP number of Petersen graph, complete graphs and twisted cubes are obtained, respectively.

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Acknowledgments

This work is supported by the Scientific Research Fund of the Science and Technology Program of Guangzhou, China (No. 201510010265), by the National Natural Science Foundation of China (No. 11551003 ) and by the Qinghai Province Natural Science Foundation (No. 2015-ZJ-911).

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Authors and Affiliations

  1. School of Mathematical Science, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Yan Liu & Weiwei Liu

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  1. Yan Liu
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  2. Weiwei Liu
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Correspondence to Yan Liu.

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Liu, Y., Liu, W. Fractional matching preclusion of graphs. J Comb Optim 34, 522–533 (2017). https://doi.org/10.1007/s10878-016-0077-x

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  • DOI: https://doi.org/10.1007/s10878-016-0077-x

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