Minimum saturated graphs without 4-cycles and 5-cycles

Given a family of graphs F, a graph G is said to be F-saturated if G does not contain a copy of F as a subgraph for any F∈F, but the addition of any edge e∉E(G) creates at least one copy of some F∈F within G. The minimum size of an F-saturated graph on n vertices is called the saturation number, den...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 12; p. 114690
Main Author Ma, Yue
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
Cycle
Saturation number
Saturation number
Cycle
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Summary:Given a family of graphs F, a graph G is said to be F-saturated if G does not contain a copy of F as a subgraph for any F∈F, but the addition of any edge e∉E(G) creates at least one copy of some F∈F within G. The minimum size of an F-saturated graph on n vertices is called the saturation number, denoted by sat(n,F). Let Cr be the cycle of length r. In this paper, we study on sat(n,F) when F is a family of cycles. In particular, we determine that sat(n,{C4,C5})=⌈5n4−32⌉ for any positive integer n.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114690