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What do Eulerian and Hamiltonian cycles have to do with genome assembly? [PDF]
PLoS Comput Biol, 2021 Many students are taught about genome assembly using the dichotomy between the complexity of finding Eulerian and Hamiltonian cycles (easy versus hard, respectively).
Medvedev P, Pop M.
europepmc +2 more sources
Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture. [PDF]
J Graph Theory, 2021 We study the existence of hamiltonian cycles in plane cubic graphs G having a facial 2‐factor Q . Thus hamiltonicity in G is transformed into the existence of a (quasi) spanning tree of faces in the contraction G ∕ Q .
Bagheri Gh B +3 more
europepmc +3 more sources
Graphs with few Hamiltonian Cycles [PDF]
Mathematics of Computation, 2018 We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number k ≥ 0 of hamiltonian cycles, which is especially efficient for small k.
J. Goedgebeur +2 more
semanticscholar +3 more sources
Discrete Mathematics, 2021 If the line graph of a graph $G$ decomposes into Hamiltonian cycles, what is $G$? We answer this question for decomposition into two cycles.
Vaidy Sivaraman, T. Zaslavsky
semanticscholar +4 more sources
Hamiltonian Cycles in Polyhedral Maps [PDF]
Proceedings - Mathematical Sciences, 2014 We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.
Maity, Dipendu, Upadhyay, Ashish Kumar
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A Tight Lower Bound for Counting Hamiltonian Cycles via Matrix Rank [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2017 For even $k$, the matchings connectivity matrix $\mathbf{M}_k$ encodes which pairs of perfect matchings on $k$ vertices form a single cycle. Cygan et al.
Curticapean, Radu +2 more
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Hamiltonian cycles and subsets of discounted occupational measures [PDF]
Mathematics of Operations Research, 2019 We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated with the input ...
Eshragh, Ali +3 more
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Tverberg’s Theorem, Disks, and Hamiltonian Cycles [PDF]
Annals of Combinatorics, 2020 For a finite set of S points in the plane and a graph with vertices on S, consider the disks with diameters induced by the edges. We show that for any odd set S, there exists a Hamiltonian cycle for which these disks share a point, and for an even set S,
P. Sober'on, Yaqian Tang
semanticscholar +5 more sources
Hamiltonian Cycles on Random Eulerian Triangulations [PDF]
Nuclear Physics B, 1998 A random Eulerian triangulation is a random triangulation where an even number of triangles meet at any given vertex. We argue that the central charge increases by one if the fully packed O(n) model is defined on a random Eulerian triangulation instead ...
Ambjorn +38 more
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Hamiltonian cycles in k ‐partite graphs [PDF]
Journal of Graph Theory, 2017 Chen et al determined the minimum degree threshold for which a balanced k ‐partite graph has a Hamiltonian cycle. We give an asymptotically tight minimum degree condition for Hamiltonian cycles in arbitrary k ‐partite graphs in that all parts have at ...
Louis DeBiasio +3 more
semanticscholar +5 more sources