Results 281 to 290 of about 78,303 (310)

Hamiltonian Cycles and Tight Cutsets

Graphs and Combinatorics
Let \(G\) be a graph. A cutset \(S\) of \(G\) is tight if \(|S|=c(G-S)\). The authors define a reduction step in \(G\) to be the deletion of all edges joining two vertices that lie together in a tight cutset, making each tight cutset independent. The (Hamiltonian) reduction \(R(G)\) of a 1-tough graph \(G\) is the iterative application of reduction ...
Viswanathan B. N, Douglas B. West
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Non‐Hamiltonian Cycles in Tournaments

Journal of Graph Theory
ABSTRACTA cycle is said to be directed if all its arcs have the same direction. Otherwise, it is said to be nondirected. A strong tournament is a tournament containing a directed path from any vertex to any other vertex. A tournament that is not strong is said to be reducible.
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Essential independent sets and Hamiltonian cycles

Journal of Graph Theory, 1996
A set \(S\) of vertices in a (finite, undirected, simple) graph \(G\) is said to be essential independent iff \(S\) is independent and contains two distinct vertices the distance of which is two in \(G\). Denoting the degree of a vertex \(x\) in \(G\) by \(d(x)\) the author proves the following theorem: Let \(k\geq 2\) and \(G\) be a \(k\)-connected ...
Chen, Guantao, Egawa, Yoshimi, Liu, Xin, Saito, Akira   +3 more
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The Square of a Hamiltonian Cycle

SIAM Journal on Discrete Mathematics, 1994
All graphs considered in this paper are simple and undirected. For a given graph \(G= (V,E)\) we denote by \(\delta(G)\) the minimum degree of \(G\). A \(k\)-chord of a cycle \(C\) is an edge joining two vertices of distance \(k\) on \(C\). The \(k\)th power of \(C\) is the graph obtained by joining every pair of vertices with distance at most \(k\) on
Fan, Genghua, Häggkvist, Roland
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Andreas Björklund: Hamiltonian Cycles

2013
This chapter outlines Bjorklund’s paper at the FOCS 2010 conference, which solved a decades-old problem about Hamiltonian cycles in graphs. Sums of determinants of randomly extended matrices are key to breaking a power-of-2 barrier in algorithmic running time for detecting these cycles.
Richard J. Lipton, Kenneth W. Regan
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Hamiltonian Paths and Cycles

2013
In this chapter, the concepts of Hamiltonian paths and Hamiltonian cycles are discussed. In the first section, the history of Hamiltonian graphs is described, and then some concepts such as Hamiltonian paths, Hamiltonian cycles, traceable graphs, and Hamiltonian graphs are defined.
Mahtab Hosseininia, Faraz Dadgostari
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Cell cycle control in cancer

Nature Reviews Molecular Cell Biology, 2021
Helen K Matthews, Cosetta Bertoli, Robertus A M De Bruin   +2 more
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The marine nitrogen cycle: new developments and global change

Nature Reviews Microbiology, 2022
David A Hutchins, Douglas G Capone
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Human and environmental safety of carbon nanotubes across their life cycle

Nature Reviews Materials, 2023
Dana Goerzen, Matteo Pasquali
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The biofilm life cycle: expanding the conceptual model of biofilm formation

Nature Reviews Microbiology, 2022
Karin Sauer, Paul Stoodley, Darla M Goeres   +2 more
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