Results 21 to 30 of about 3,188,937 (280)
Number of Hamiltonian Cycles in Planar Triangulations [PDF]
SIAM Journal on Discrete Mathematics, 2021 Whitney proved in 1931 that 4-connected planar triangulations are Hamiltonian. Hakimi, Schmeichel, and Thomassen conjectured in 1979 that if $G$ is a 4-connected planar triangulation with $n$ vertices then $G$ contains at least $2(n-2)(n-4)$ Hamiltonian ...
Xiaonan Liu, Xingxing Yu
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High powers of Hamiltonian cycles in randomly augmented graphs [PDF]
Journal of Graph Theory, 2020 We investigate the existence of powers of Hamiltonian cycles in graphs with large minimum degree to which some additional edges have been added in a random manner.
Sylwia Antoniuk +4 more
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Finding hidden hamiltonian cycles [PDF]
Random Structures & Algorithms, 1991 AbstractConsider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that “high” the cycle. Is it possible to unravel the structures, that is, to efficiently find a Himiltonian cycle in G? We describe an O(n3 log n)‐step algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly
Broder, Andrei Z. +2 more
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Sharp thresholds for nonlinear Hamiltonian cycles in hypergraphs [PDF]
Random Struct. Algorithms, 2019 For positive integers r>ℓ, an r‐uniform hypergraph is called an ℓ‐cycle if there exists a cyclic ordering of its vertices such that each of its edges consists of r consecutive vertices, and such that every pair of consecutive edges (in the natural ...
Bhargav P. Narayanan, M. Schacht
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Enumerating Hamiltonian Cycles [PDF]
The Electronic Journal of Combinatorics, 2014 A dynamic programming method for enumerating hamiltonian cycles in arbitrary graphs is presented. The method is applied to grid graphs, king's graphs, triangular grids, and three-dimensional grid graphs, and results are obtained for larger cases than previously published.
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Powers of Hamiltonian cycles in randomly augmented graphs [PDF]
Random Struct. Algorithms, 2018 We study the existence of powers of Hamiltonian cycles in graphs with large minimum degree to which some additional edges have been added in a random manner. It follows from the theorems of Dirac and of Komlós, Sarközy, and Szemerédi that for every k ≥ 1
Andrzej Dudek +3 more
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Orientations of hamiltonian cycles in large digraphs [PDF]
, 1986 We prove that, with some exceptions, every digraph with n ≥ 9 vertices and at least (n - 1) (n - 2) + 2 arcs contains all orientations of a Hamiltonian ...
Adam Pawel Wojda +3 more
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Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials [PDF]
, 2012 In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials.
Gao, Bin +2 more
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A pair degree condition for Hamiltonian cycles in 3-uniform hypergraphs [PDF]
Combinatorics, probability & computing, 2019 We prove a new sufficient pair degree condition for tight Hamiltonian cycles in $3$ -uniform hypergraphs that (asymptotically) improves the best known pair degree condition due to Rödl, Ruciński, and Szemerédi.
B. Schülke
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Proper Hamiltonian Cycles in Edge-Colored Multigraphs [PDF]
, 2017 A $c$-edge-colored multigraph has each edge colored with one of the $c$ available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges ...
Borozan, Valentin +4 more
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