Cycle Lengths of Hamiltonian Pℓ-free Graphs

For an integer ℓ at least three, we prove that every Hamiltonian P ℓ -free graph G on n > ℓ vertices has cycles of at least 2 ℓ n - 1 different lengths. For small values of ℓ , we can improve the bound as follows. If 4 ≤ ℓ ≤ 7 , then G has cycles of at least 1 2 n - 1 different lengths, and if ℓ...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 31; no. 6; pp. 2335 - 2345
Main Authors Meierling, Dirk, Rautenbach, Dieter
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 05.11.2014
Subjects
Combinatorics
Engineering Design
Mathematics
Mathematics and Statistics
Original Paper
Cycle length
Cycle spectrum
05C45
Hamiltonian cycle
05C38
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Summary:For an integer ℓ at least three, we prove that every Hamiltonian P ℓ -free graph G on n > ℓ vertices has cycles of at least 2 ℓ n - 1 different lengths. For small values of ℓ , we can improve the bound as follows. If 4 ≤ ℓ ≤ 7 , then G has cycles of at least 1 2 n - 1 different lengths, and if ℓ is 4 or 5 and n is odd, then G has cycles of at least n - ℓ + 2 different lengths.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-014-1494-1