【摘 要】
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In 1976, Thomassen C.conjectures that every longest cycle in a 3-connected graph has a chord (see Bondy J.A., Murty U.S.R., Graph theory, Graduate Texts in Math
【机 构】
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SchoolofMathematicsandStatistics,MinnanNormalUniversity,Zhangzhou,Fujian363000,CHINA
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In 1976, Thomassen C.conjectures that every longest cycle in a 3-connected graph has a chord (see Bondy J.A., Murty U.S.R., Graph theory, Graduate Texts in Mathematics, 244, Springer, New York, 2008, Unsolved Problems 65).In 1979, Kotzig A.conjectures that there exists no graph in which each pair of vertices is connected by a unique path of length k (k ≥ 3) (see Bondy J.A., Murty U.S.R., Graph theory,Graduate Texts in Mathematics, 244, Springer, New York, 2008, Unsolved Problems 64).Let G be a connected graph with p vertices and q edges and define the parameter r =q-p + 1.The maximum number of cycles in such a graph is denoted by Ψ(r).In 1981, Entringer R.C.and Slater P.J raised the problem of determining Ψ(r) (see Entringer R.C., Slater P.J, On the maximum number of cycles in a graph, Ars Combin.11 (1981), 289-294).This talk summarizes some results on these problem and the conjectures that relate to these.
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