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Hamiltonian cycle problem and Markov chains
, 2014 This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be ...
Nguyen, Giang T +3 more
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A Conjecture on Rainbow Hamiltonian Cycle Decomposition [PDF]
Wu in 1999 conjectured that if $H$ is a subgraph of the complete graph $K_{2n+1}$ with $n$ edges, then there is a Hamiltonian cycle decomposition of $K_{2n+1}$ such that each edge of $H$ is in a separate Hamiltonian cycle.
Miralaei, Meysam, Javadi, Ramin
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Planar Hamiltonian Chordal Graphs are Cycle Extendible
, 1997 A cycle C in a graph G is extendible if there exists a cycle C 0 in G such that V (C) ` V (C 0 ) and jV (C 0 )j = jV (C)j + 1. A graph G is cycle extendible if G contains at least one cycle and every nonhamiltonian cycle in G is extendible. A graph
Tao Jiang
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A generalization of Hamiltonian cycles for trees [PDF]
Czechoslovak Mathematical Journal, 1976 openaire +1 more source
Addendum to “Ring elements as sums of units”
Open Mathematics, 2013 Lanski Charles, Maróti Attila
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On Hamiltonian Cycles and Hamiltonian Paths
Information Processing Letters, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammad Sohel Rahman, M Kaykobad
exaly +3 more sources
The Square of a Hamiltonian Cycle
SIAM Journal on Discrete Mathematics, 1994Let C be a cycle. The square of C is the graph obtained by joining every pair of vertices of distance 2 in C. Let G be a graph on n vertices with minimum degree $\delta ( G )$. This paper proves that, if $\delta ( G ) \geq \frac{5}{7}n$, then G contains the square of a Hamiltonian cycle.
Genghua Fan, Roland Häggkvist
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Hamiltonian Cycles and Markov Chains
Mathematics of Operations Research, 1994In this paper we derive new characterizations of the Hamiltonian cycles of a directed graph, and a new LP-relaxation of the Traveling Salesman Problem. Our results are obtained via an embedding of these combinatorial optimization problems in suitably perturbed controlled Markov chains.
Filar, JA, Krass, D
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A Remark on Hamiltonian Cycles
Mathematische Nachrichten, 1992AbstractLet G be an undirected and simple graph on n vertices. Let ω, α and χ denote the number of components, the independence number and the connectivity number of G. G is called a 1‐tough graph if ω(G – S) ⩽ |S| for any subset S of V(G) such that ω(G − S) > 1.
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On Hamiltonian cycles in the FCC grid
Computers & Graphics, 2020Abstract The face centered cubic (FCC) grid is a space-filling grid, one of the alternatives to the traditional cubic one. We show that there are five Hamiltonian cycles (non-equivalent up to rotation and symmetry), connecting the faces of a voxel in the FCC grid.
Lidija Comic, Paola Magillo
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