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- W2061081952 abstract "We study the set of cycle lengths in a hamiltonian graph G of order n with two fixed and nonadjacent vertices x , y whose degree sum satisfies d ( x )+ d ( y )⩾ n + z , where z ⩾1. We prove that this set contains all integers between 3 and 4n+4z+32 19 . This improves and generalizes some results of Faudree et al. (Discuss. Math. Graph Theory 16 (1996) 27) and Schelten and Schiermeyer (Discrete Appl. Math. 79 (1997) 201). We also show that if z⩾ 5 18 n then G contains a cycle of length p for every p satisfying 3⩽p⩽ n 2 + z 2 +1 ." @default.
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- W2061081952 date "2004-09-01" @default.
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- W2061081952 title "On the structure of the set of cycle lengths in a hamiltonian graph" @default.
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- W2061081952 doi "https://doi.org/10.1016/j.disc.2003.11.053" @default.
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