Sparse connected graphs with at most n(1+1/(204k^3+126k^2)) edges are shown to have Ramsey number 2n-1 against fans F_k, with a similar result for multiple fans.
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Fan-goodness of sparse graphs
Sparse connected graphs with at most n(1+1/(204k^3+126k^2)) edges are shown to have Ramsey number 2n-1 against fans F_k, with a similar result for multiple fans.