Removable Cycles in 2-connected Graphs of Minimum Degree at Least Four
نویسنده
چکیده
The lower bound on the length of 'removable' cycles in Theorem 1 is essentially best possible since there exist 2-connected simple graphs of minimum degree k whose longest 'removable' cycle has length k + i. Moreover, for the special case k = 4, we can construct 2-connected, 4-regular simple graphs whose longest 'removable' cycle has length four. The following counterexample which was independently constructed by N. L. Robertson [2] and the present author, shows that Hobbs' conjecture, and hence Theorem 1, does not hold for graphs in general.
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