Spectral extrema of graphs: Forbidden hexagon

To determine the Turán numbers of even cycles is a central problem of extremal graph theory. Even for C6, the Turán number is still open. Till now, the best known upper bound is given by Füredi, Naor and Verstraëte [On the Turán number for the hexagon, Advances in Math.]. In 2010, Nikiforov posed a...

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Bibliographic Details
Published inDiscrete mathematics Vol. 343; no. 10; p. 112028
Main Authors Zhai, Mingqing, Lin, Huiqiu
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2020
Subjects
Adjacency matrix
Cycle
Hexagon
Path
Spectral radius
Path
Adjacency matrix
Hexagon
Spectral radius
Cycle
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Summary:To determine the Turán numbers of even cycles is a central problem of extremal graph theory. Even for C6, the Turán number is still open. Till now, the best known upper bound is given by Füredi, Naor and Verstraëte [On the Turán number for the hexagon, Advances in Math.]. In 2010, Nikiforov posed a spectral version of extremal graph theory problem: what is the maximum spectral radius ρ of an H-free graph of order n? Let exsp(n,H)=max{ρ(G)||V(G)|=n,H⊈G}. In contrast to the unsolved problem of Turán number of C6, we obtain the exact value of exsp(n,C6) and characterize the unique extremal graph. The result also confirms Nikiforov’s conjecture [The spectral radius of graphs without paths and cycles of specified length, Linear Algebra Appl.] for k=2.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.112028