Hamiltonian cycles through prescribed edges of 4-connected maximal planar graphs
نویسندگان
چکیده
منابع مشابه
On Hamiltonian Cycles through Prescribed Edges of a Planar Graph
We use [3] for terminology and notation not defined here and consider finite simple graphs only. The first major result on the existence of hamiltonian cycles in graphs embeddable in surfaces was by H. Whitney [12] in 1931, who proved that 4-connected maximal planar graphs are hamiltonian. In 1956, W.T. Tutte [10,11] generalized Whitney’s result from maximal planar graphs to arbitrary 4-connect...
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The Hamiltonian cycle problem is one of the most popular NP-complete problems, and remains NP-complete even if we restrict ourselves to a class of (3-connected cubic) planar graphs [5,9]. Therefore, there seems to be no polynomial-time algorithm for the Hamiltonian cycle problem. However, for certain (nontrivial) classes of restricted graphs, there exist polynomial-time algorithms [3,4,6]. In f...
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We prove the result stated in the title (conjectured by Grünbaum), and a conjecture of Plummer that every graph which can be obtained from a 4–connected planar graph by deleting two vertices is Hamiltonian. The proofs are constructive and give rise to polynomial–time algorithms.
متن کاملCycles in 4-connected planar graphs
Let G be a 4-connected planar graph on n vertices. Previous results show that G contains a cycle of length k for each k ∈ {n, n − 1, n − 2, n − 3} with k ≥ 3. These results are proved using the “Tutte path” technique, and this technique alone cannot be used to obtain further results in this direction. One approach to obtain further results is to combine Tutte paths and contractible edges. In th...
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We generalize the following two seminal results. 1. Thomassen’s result [19] in 1983, which says thatevery 4-connected planar graph is hamiltonian-connected (which generalizes the old result of Tutte[20] in 1956, which says that every 4-connectedplanar graph is hamiltonian). 2. Thomas and Yu’s result [16] in 1994, which saysthat every 4-connected projective planar graph is<lb...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.10.005