... irregular graphs, Graphs and Combinatorics 18 (2002), 53–57.[2] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, secondedition, 1993.[3] J.A. Bondy, M. Simonovits, Cycles ... lower bound on thenumber of non-returning walks, by Alon, Hoory and Linial [1], which gives the best knownupper bound on ex(n, {C3,C4, ,C2k}):Proposition 6 Let G be an n-vertex graph of ... problems in graph theory, ‘Theory of Graphs and Its Applications’(M.Fiedler, Ed.), Academic Press, New York, 1965.[6] P. Erd˝os, M. Simonovits, Compactness results in extremal graph theory,...