Pairs of Hamiltonian circuits in 5-connected planar graphs
نویسندگان
چکیده
منابع مشابه
5-Connected Toroidal Graphs are Hamiltonian-Connected
The problem on the Hamiltonicity of graphs is well studied in discrete algorithm and graph theory, because of its relation to traveling salesman problem (TSP). Starting with Tutte’s result, stating that every 4-connected planar graph is Hamiltonian, several researchers have studied the Hamiltonicity of graphs on surfaces. Extending Tutte’s technique, Thomassen proved that every 4-connected plan...
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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...
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For an integer kwith k ≥ 2 and a pair of connected graphs F1 and F2 of order at least three, we say that {F1, F2} is a k-forbidden pair if every k-connected {F1, F2}-free graph, except possibly for a finite number of exceptions, is Hamiltonian. If no exception arises, {F1, F2} is said to be a strong k-forbidden pair. The 2-forbidden pairs and the strong 2-forbidden pairs are determined by Faudr...
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A graph G is said to be 4-ordered if for any ordered set of four distinct vertices of G, there exists a cycle in G that contains all of the four vertices in the designated order. Furthermore, if we can find such a cycle as a Hamiltonian cycle, G is said to be 4-ordered Hamiltonian. It was shown that every 4-connected planar triangulation is (i) Hamiltonian (by Whitney) and (ii) 4-ordered (by Go...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1976
ISSN: 0095-8956
DOI: 10.1016/0095-8956(76)90051-4