Results 21 to 30 of about 841,975 (192)
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
Andrei Z. Broder +2 more
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The Traveling Salesman Problem for Cubic Graphs
Journal of Graph Algorithms and Applications, 2007 We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2n/3) ≈ 1.260n and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound.
David Eppstein
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On Hamiltonian Cycles in Claw-Free Cubic Graphs
Discussiones Mathematicae Graph Theory, 2022 We show that every claw-free cubic graph of order n at least 8 has at most 2⌊n4⌋{2^{\left\lfloor {{n \over 4}} \right\rfloor }} Hamiltonian cycles, and we also characterize all extremal graphs.
Mohr Elena, Rautenbach Dieter
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Enforced hamiltonian cycles in generalized dodecahedra
Electronic Journal of Graph Theory and Applications, 2013 The H-force number of a hamiltonian graph G is the smallest number k with the property that there exists a set W ⊆ V (G) with |W| = k such that each cycle passing through all vertices of W is a hamiltonian cycle.
Maria Timkova
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A remark on Hamiltonian cycles
Journal of Combinatorial Theory, Series B, 1981 AbstractEvery 2-connected graph G with δ ⩾ (v + κ)3 is hamiltonian where v denotes the order, δ the minimum degree and κ the point connectivity of G.
Roland Häggkvist, G. G. Nicoghossian
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Hamiltonian Cycles in T-Graphs [PDF]
Discrete & Computational Geometry, 2000 The vertices and polygonal edges of the planar Archimedean tiling \(3^6\) of the plane is called the triangular tiling graph (TTG). A subgraph \(G\) of TTG is linearly convex if, for every line \(L\) which contains an edge of TTG, the set \(L \cap G\) is a (possibly degenerated or empty) line segment.
John R. Reay, Tudor Zamfirescu
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Hamiltonian colorings of graphs with long cycles [PDF]
, 2003 summary:By a hamiltonian coloring of a connected graph $G$ of order $n \ge 1$ we mean a mapping $c$ of $V(G)$ into the set of all positive integers such that $\vert c(x) - c(y)\vert \ge n - 1 - D_G(x, y)$ (where $D_G(x, y)$ denotes the length of a ...
Nebeský, Ladislav
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Second Hamiltonian Cycles in Claw-Free Graphs
Theory and Applications of Graphs, 2015 Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and ...
Hossein Esfandiari +3 more
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Arc-Disjoint Hamiltonian Paths in Strong Round Decomposable Local Tournaments
Discussiones Mathematicae Graph Theory, 2021 Thomassen, [Edge-disjoint Hamiltonian paths and cycles in tournaments, J. Combin. Theory Ser. B 28 (1980) 142–163] proved that every strong tournament has a pair of arc-disjoint Hamiltonian paths with distinct initial vertices and distinct terminal ...
Meng Wei
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Limit cycles of planar piecewise linear Hamiltonian differential systems with two or three zones
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we study the existence of limit cycles in continuous and discontinuous planar piecewise linear Hamiltonian differential system with two or three zones separated by straight lines and such that the linear systems that define the piecewise ...
Claudio Pessoa, Ronisio Ribeiro
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