Corpus ID: 237498956

# An explicit construction of graphs of bounded degree that are far from being Hamiltonian

@inproceedings{Adler2020AnEC,
title={An explicit construction of graphs of bounded degree that are far from being Hamiltonian},
year={2020}
}
• Published 2020
• Computer Science
Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding decision problem, that asks whether a given graph is Hamiltonian (i. e. admits a Hamiltonian cycle), is one of Karp’s famous NP-complete problems. In this paper we study graphs of bounded degree that are far from being Hamiltonian, where a graph G on n vertices is… Expand
1 Citations

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#### References

SHOWING 1-10 OF 29 REFERENCES
Computing and Testing Small Connectivity in Near-Linear Time and Queries via Fast Local Cut Algorithms
• Computer Science, Mathematics
• SODA
• 2020
This paper presents a slack variant of the cut-detection problem in a directed graph where, when such a cut exists, it can output a cut with up to $O(k\nu)$ edges reachable from $x$. Expand
On Testing Hamiltonicity in the Bounded Degree Graph Model
• Oded Goldreich
• Computer Science, Mathematics
• Electron. Colloquium Comput. Complex.
• 2020
We show that testing Hamiltonicity in the bounded-degree graph model requires a linear number of queries. This refers to both the path and the cycle versions of the problem, and similar results holdExpand
On the characterization of 1-sided error strongly testable graph properties for bounded-degree graphs
• Mathematics, Computer Science
• computational complexity
• 2020
This work gives a characterization of the 1-sided error strongly testable monotone graph properties and the 1 -sided error strong testable hereditary graph properties in all the bounded-degree directed and undirected graphs models. Expand
Random walks and forbidden minors II: a poly(d ε-1)-query tester for minor-closed properties of bounded degree graphs
• Computer Science, Mathematics
• STOC
• 2019
This paper is a continuation of recent work of the authors (FOCS 2018) analyzing random walk algorithms that find forbidden minors, using techniques from spectral graph theory to resolve the open question of property testing P. Expand
Testing subdivision-freeness: property testing meets structural graph theory
• Computer Science, Mathematics
• STOC '13
• 2013
It is shown that, for any integer t ≥ 1, Kt-subdivision-freeness is testable with a constant number of queries in the bounded-degree model, which was not previously known to be testable even with o(n) queries. Expand
Triangle mesh compression along the Hamiltonian cycle
• Mathematics, Computer Science
• The Visual Computer
• 2013
This paper proposes a novel and efficient algorithm for single-rate compression of triangle meshes that can be encoded by a face label sequence with low entropy containing only four kinds of labels (HETS) and the transmission delay at the decoding end that frequently occurs in the conventional single- rate approaches is obviously reduced. Expand
An Efficient Hamiltonian-cycle power-switch routing for MTCMOS designs
• Engineering, Computer Science
• 17th Asia and South Pacific Design Automation Conference
• 2012
This paper proposes an efficient power-switch routing framework, which can effectively and efficiently find a feasible Hamiltonian-cycle routing among power switches without violating the Manhattan distance constraint between any two power switches while handling the irregular placement of the power switches resulting from the hard macros. Expand
Every property of hyperfinite graphs is testable
• Mathematics, Computer Science
• STOC '11
• 2011
It is shown that the structure of a planar graph on large enough number of vertices, n, and with constant maximum degree d, is determined, up to the modification (insertion or deletion) of at most ε d n edges, by the frequency of k-discs for certain k=k(ε,d) that is independent of the size of the graph. Expand
Property Testing on k-Vertex-Connectivity of Graphs
• Mathematics, Computer Science
• Algorithmica
• 2010
The algorithm is the first constant-time k-vertex-connectivity testing algorithm for general k≥4 and runs in $O(d(\frac{c}{\epsilon d})$ time (c>1 is a constant) for (k−1)- Vertex-connected graphs, and in time ( c>1) for general graphs. Expand
Query-Number Preserving Reductions and Linear Lower Bounds for Testing
• Computer Science
• IEICE Trans. Inf. Syst.
• 2010
This paper introduces two reductions that preserve the query complexity of testing algorithms for various problems, including basic NP-complete properties, 3-edge-colorability, directed Hamiltonian path/cycle, undirected Hamiltonians path/ cycle,3-dimensional matching andNP-complete generalized satisfiability problems. Expand