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- W3201704520 abstract "In a recent paper, Gerbner, Patkós, Tuza and Vizer studied regular F-saturated graphs. One of the essential questions is given F, for which n does a regular n-vertex F-saturated graph exist. They proved that for all sufficiently large n, there is a regular K3-saturated graph with n vertices. We extend this result to both K4 and K5 and prove some partial results for larger complete graphs. Using a variation of sum-free sets from additive combinatorics, we prove that for all k≥2, there is a regular C2k+1-saturated with n vertices for infinitely many n. Studying the sum-free sets that give rise to C2k+1-saturated graphs is an interesting problem on its own and we state an open problem in this direction." @default.
- W3201704520 created "2021-10-11" @default.
- W3201704520 creator A5056721527 @default.
- W3201704520 date "2022-01-01" @default.
- W3201704520 modified "2023-09-26" @default.
- W3201704520 title "Regular saturated graphs and sum-free sets" @default.
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- W3201704520 doi "https://doi.org/10.1016/j.disc.2021.112659" @default.
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