Long Cycles in 3-Connected Graphs
نویسندگان
چکیده
منابع مشابه
Long Cycles in 3-Connected Graphs
Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Ω(nlog3 2). In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the projective plane, or the torus, or the Klein bottle. MSC Primary 05C38 and 05C50 Secondary 57M15 Partially supported by NSA grant ...
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In this paper we apply a cutting theorem of Thomassen to show that there is a function f : N→ N such that if G is a 3-connected graph which can be embedded in the orientable surface of genus g with face-width at least f(g), then G contains a cycle of length at least c(n3 ), where c is a constant not dependent on g. MSC Primary 05C38 and 05C50 Secondary 57M15 Partially supported by NSF grant DMS...
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This result is best possible for k = 3 since the Petersen graph is a nonhamiltonian, 2-connected, 3-regular graph on 10 vertices. It is essentially best possible for k > 4 since there exist non-hamiltonian, 2-connected, kregular graphs on 3k + 4 vertices for k even, and 3k + 5 vertices for all k. Examples of such graphs are given in [ 1, 3 1. The problem of determining the values of k for which...
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I n t r o d u c t i o n . In this paper, we s tudy the following quest ion: How long a cycle must there be in a 3-connected 3-regular graph on n vertices? For planar graphs this question goes back to T a i t [6], who conjectured tha t any planar 3-connected 3-regular graph is hamiltonian. T u t t e [7] disproved this conjecture by finding a counterexample on 46 vertices. Using Tu t t e ' s exam...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2002
ISSN: 0095-8956
DOI: 10.1006/jctb.2002.2113