Spectral radius and the 2-power of Hamilton cycle

Spectral radius and the 2-power of Hamilton cycle

For a graph G on n⩾18 vertices and e(G) edges that does not contain the 2-power of a Hamilton cycle Cn2, we identify all the graphs G with e(G)=ex(n,Cn2)−1 and e(G)=ex(n,Cn2)−2, respectively, where ex(n,Cn2) is the Turán number of Cn2. This extends the result of Khan and Yuan [Discrete Math. 345 (20...

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Veröffentlicht in:Discrete mathematics 2023-01, Vol.346 (1), p.113155, Article 113155
Hauptverfasser: Yan, Xinru, He, Xiaocong, Feng, Lihua, Liu, Weijun
Format: Artikel
Sprache:eng
Schlagworte:
2-power
Extremal graph
Hamilton cycle
Spectral radius
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Zusammenfassung:For a graph G on n⩾18 vertices and e(G) edges that does not contain the 2-power of a Hamilton cycle Cn2, we identify all the graphs G with e(G)=ex(n,Cn2)−1 and e(G)=ex(n,Cn2)−2, respectively, where ex(n,Cn2) is the Turán number of Cn2. This extends the result of Khan and Yuan [Discrete Math. 345 (2022) 112908.]. Using this result, we establish a spectral condition for a graph containing Cn2.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2022.113155