A linear algorithm for finding Hamiltonian cycles in 4-connected maximal planar graphs
نویسندگان
چکیده
منابع مشابه
A linear algorithm for finding Hamiltonian cycles in 4-connected maximal planar graphs
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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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 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.
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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...
متن کاملAn efficient algorithm to find a Hamiltonian circuit in a 4-connected maximal planar graph
This paper describes an efficient algorithm to find a Hamiltonian circuit in an arbitrary 4-connected maximal planar graph. The algorithm is based on our simlplified version of Whitney's proof of his theorem: every 4-connected maximal planar graph has a Hamiltonian circuit.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1984
ISSN: 0166-218X
DOI: 10.1016/0166-218x(84)90109-4