Abstract
Let C be a longest cycle in the 3-connected graph G and let H be a component of G - V(C) such that ¦V(H)¦≥ 3. We supply estimates of the form ¦C¦ ≥ 2d(u) + 2d(v) − a (4 ≤ a ≤ 8), where u, v are suitably chosen non-adjacent vertices in G.
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References
G.A. Dirac, Some Theorems on Abstract Graphs. Proc. London Math. Soc. (3)2(1952), 69-81.
H.J. Voss, Bridges of Longest Circuits and of Longest Paths in Graph. In: Beiträge zur Graphentheorie und deren Anwendungen, Internat. Koll. Graphentheorie Oberhof (DDR)10–16 April 1977, 275-286.
H.A. Jung, Longest Circuits in 3-connected Graphs. In: Finite and Infinite Sets, Vol.I (Eger, 1981, edited by A. Hajnal and V.T. Sos), Coll. Math. Soc. J. Bolyai 37, North-Holland Publ. Comp., Amsterdam, 1984, 403–438.
H.A. Jung, Longest Cycles in Graphs with Moderate Connectivity. In: Topics in Combinatorics and Graph Theory, essays in Honour of Gerhard Ringel (edited by R. Bodendiek and R. Henn), Physica-Verlag, Heidel-berg(1990), 765–777.
H.A. Jung, Longest Paths Joining Given Vertices in a Graph. Abh. Math. Sem. Uni. Hamburg 56(1986), 127–137.
H. Enomoto, Long Paths and Large Cycles in Finite Graphs. J. Graph Theory 8(1984), 287–301.
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Jung*, H.A., Vumar, E. On the Circumference of 3-connected Graphs. Results. Math. 41, 118–127 (2002). https://doi.org/10.1007/BF03322759
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DOI: https://doi.org/10.1007/BF03322759