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International Conference on Mathematical Aspects of Computer and Information Sciences

MACIS 2019: Mathematical Aspects of Computer and Information Sciences pp 280–287Cite as

Edge-Critical Equimatchable Bipartite Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11989))

Abstract

A graph is called equimatchable if all of its maximal matchings have the same size. Lesk et al. [6] provided a characterization of equimatchable bipartite graphs. Since this characterization is not structural, Frendrup et al. [4] also provided a structural characterization for equimatchable graphs with girth at least five; in particular, a characterization for equimatchable bipartite graphs with girth at least six. In this work, we extend the partial characterization of Frendrup et al. [4] to equimatchable bipartite graphs without any restriction on girth. For an equimatchable graph, an edge is said to be critical-edge if the graph obtained by removal of this edge is not equimatchable. An equimatchable graph is called edge-critical if every edge is critical. Reducing the characterization of equimatchable bipartite graphs to the characterization of edge-critical equimatchable bipartite graphs, we give two characterizations of edge-critical equimatchable bipartite graphs.

This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under grant no. 118E799. The work of Didem Gözüpek was supported by the BAGEP Award of the Science Academy of Turkey.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Gebze Technical University, Gebze, Kocaeli, Turkey

    Yasemin Büyükçolak & Sibel Özkan

  2. Department of Computer Engineering, Gebze Technical University, Gebze, Kocaeli, Turkey

    Didem Gözüpek

Authors
  1. Yasemin Büyükçolak
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  2. Didem Gözüpek
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  3. Sibel Özkan
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Corresponding author

Correspondence to Yasemin Büyükçolak .

Editor information

Editors and Affiliations

  1. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

  2. IMJ-PRG, Sorbonne University, Paris, France

    Elias Tsigaridas

  3. Institute of Information Technologies, Gebze Technical University, Gebze, Turkey

    Zafeirakis Zafeirakopoulos

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Büyükçolak, Y., Gözüpek, D., Özkan, S. (2020). Edge-Critical Equimatchable Bipartite Graphs. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_21

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  • DOI: https://doi.org/10.1007/978-3-030-43120-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43119-8

  • Online ISBN: 978-3-030-43120-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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