Packing of the k-power of Hamilton cycles

The k-power of a Hamilton cycle is obtained from it by adding edges between all two vertices whose distance in it is at most k. For sufficiently large n, we determine the maximum number of edges of an n-vertex graph without containing the k-power of a Hamilton cycle, and identify all n-vertex graphs...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 12; p. 114630
Main Authors Chen, Wanfang, Lu, Changhong, Wu, Qi, Yuan, Long-Tu
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
Hamilton cycle
k-power of graphs
Packing
Packing
Hamilton cycle
k-power of graphs
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Summary:The k-power of a Hamilton cycle is obtained from it by adding edges between all two vertices whose distance in it is at most k. For sufficiently large n, we determine the maximum number of edges of an n-vertex graph without containing the k-power of a Hamilton cycle, and identify all n-vertex graphs with at most n−2k+ℓ edges which do not pack with the k-power of a Hamilton cycle.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114630