1996
DOI: 10.1016/0012-365x(95)00173-t
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Cycle-saturated graphs of minimum size

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Cited by 22 publications
(48 citation statements)
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“…where ε(k) = 2 for k even ≥ 10, ε(k) = 3 for k odd ≥ 17. Although there is still a gap, Theorem 2.1 supersedes all earlier results for k ≥ 6 except the construction giving sat(n, C 6 ) ≤ 3 2 n for n ≥ 11 from [3]. Our new construction for a k-cycle-saturated graph for n = (k − 1) + t(k − 4), where k ≥ 7, t ≥ 1, can be read from the picture below.…”
Section: Theorem 21mentioning
confidence: 52%
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“…where ε(k) = 2 for k even ≥ 10, ε(k) = 3 for k odd ≥ 17. Although there is still a gap, Theorem 2.1 supersedes all earlier results for k ≥ 6 except the construction giving sat(n, C 6 ) ≤ 3 2 n for n ≥ 11 from [3]. Our new construction for a k-cycle-saturated graph for n = (k − 1) + t(k − 4), where k ≥ 7, t ≥ 1, can be read from the picture below.…”
Section: Theorem 21mentioning
confidence: 52%
“…Thus, divide V(G) into five parts {X,Y3,Y4+,Z2,Z3+}, truerightY3:={vY:prefixdegG(v)=3}0.28em and Y4+:={vY:prefixdegG(v)4},rightZ2:={vZ:prefixdegG(v)=2}0.28em and Z3+:={vZ:prefixdegG(v)3}. Lemma ( The structure of Ck‐ saturated graphs . See ). Suppose that G is a Ck‐ saturated graph ( and k5).…”
Section: Degree One Vertices In (Semi)saturated Graphsmentioning
confidence: 99%
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“…Barefoot et al [1] gave an asymptotic value of mx(n, C k ). They proved that for any natural number k and sufficiently large n, n + an k mx(n, C k ) n + bn k for some positive constants a and b.…”
Section: Introductionmentioning
confidence: 98%
“…Very recently, Chen [9,8] completely solved the case of C 5 . The value of sat(n, C m ) is unknown (even asymptotically) for any other fixed m; various bounds are proved in [1,17]. Also, the aggregate outcome of papers [6,19,11,10,12,32], with the final gaps filled by computer search, determines sat(n, C n ), the Hamilton cycle case, for all n ≥ 3.…”
mentioning
confidence: 99%