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Linear and Multilinear Algebra Volume 67, 2019 - Issue 12
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Articles

Fractional matching number and eigenvalues of a graph

Jie XueDepartment of Computer Science and Technology, East China Normal University, Shanghai, People's Republic of ChinaView further author information
,
Mingqing ZhaiDepartment of Mathematics, Chuzhou University, Chuzhou, People's Republic of ChinaView further author information
&
Jinlong ShuDepartment of Computer Science and Technology, East China Normal University, Shanghai, People's Republic of ChinaCorrespondence[email protected]
[email protected]
View further author information
Pages 2565-2574 | Received 23 Apr 2017, Accepted 03 Jul 2018, Published online: 20 Jul 2018

References

  • Scheinerman ER, Ullman DH. Fractional graph theory: a rational approach to the theory of graphs. New York: Wiley & Sons; 1997.
  • Behrend RE, O S, West DB. Sharp lower bounds on the fractional matching number. Discrete Appl Math. 2015;186:272–274.
  • Choi I, Kim J, O S. The difference and ratio of the fractional matching number and the matching number of graphs. Discrete Math. 2016;339:1382–1386.
  • Cioabǎ SM. Perfect matchings, eigenvalues and expansion. C R Math Acad Sci Soc R Can. 2005;27:101–104.
  • Cioabǎ SM, Gregory DA. Large matchings from eigenvalues. Linear Algebra Appl. 2007;422:308–317.
  • Cioabǎ SM, Gregory DA, Haemers WH. Matchings in regular graphs from eigenvalues. J Combin Theory Ser B. 2009;99:287–297.
  • Feng L, Cao J, Liu W, et al. The spectral radius of edge chromatic critical graphs. Linear Algebra Appl. 2016;492:78–88.
  • Gu X, Lai H-J, Li P, et al. Edge-disjoint spanning trees, edge connectivity and eigenvalues in graphs. J Graph Theory. 2016;81:16–29.
  • Haemers WH. Interlacing eigenvalues and graphs. Linear Algebra Appl. 1995;227–228:593–616.
  • Li B, Ning B. Spectral analogues of Erdős' and Moon–Moser's theorems on Hamilton cycles. Linear Multilinear Algebra. 2016;64:2252–2269.
  • Li R. Eigenvalues, Laplacian eigenvalues and some Hamiltonian properties of graphs. Util Math. 2012;88:247–257.
  • Li R. Spectral conditions for some stable properties of graphs. J Combin Math Combin Comput. 2014;88:199–205.
  • Liu R, Shiu WC, Xue J. Sufficient spectral conditions on Hamiltonian and traceable graphs. Linear Algebra Appl. 2015;467:254–266.
  • Lu M, Liu H, Tian F. Spectral radius and Hamiltonian graphs. Linear Algebra Appl. 2012;437:1670–1674.
  • O S. Spectral radius and fractional matchings in graphs. European J Combin. 2016;55:144–148.
  • O S Cioabǎ SM. Edge-connectivity, eigenvalues, and matchings in regular graphs. SIAM J Discrete Math. 2010;24:1470–1481.
  • Brouwer AE, Haemers WH. Eigenvalues and perfect matchings. Linear Algebra Appl. 2005;395:155–162.
  • Berge C. Théorie des graphes et ses applications (French) Collection Universitaire de Mathématiques. Paris: II Dunod; 1958.
  • Anderson WN, Morley TD. Eigenvalues of the Laplacian of a graph. Linear Multilinear Algebra. 1985;18:141–145.

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