Upper bounds on ex(J(n;k,k+1),C_{2r}) are derived, implying that C_{2r}-free subgraphs of the doubled odd graph have o(total edges) for r≥6.
Erd ˝os, Some of my favourite unsolved problems, in: A tribute to Paul Erd ˝os, Cambridge Uni- versity Press, (1990) 467–478
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On even-cycle-free subgraphs of the doubled Johnson graphs
Upper bounds on ex(J(n;k,k+1),C_{2r}) are derived, implying that C_{2r}-free subgraphs of the doubled odd graph have o(total edges) for r≥6.