# Simple Necessary Conditions for the Existence of a Hamiltonian Path with Applications to Cactus Graphs

@article{Welke2017SimpleNC, title={Simple Necessary Conditions for the Existence of a Hamiltonian Path with Applications to Cactus Graphs}, author={Pascal Welke}, journal={ArXiv}, year={2017}, volume={abs/1709.01367} }

We describe some necessary conditions for the existence of a Hamiltonian path in any graph (in other words, for a graph to be traceable). These conditions result in a linear time algorithm to decide the Hamiltonian path problem for cactus graphs. We apply this algorithm to several molecular databases to report the numbers of graphs that are traceable cactus graphs.

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## References

SHOWING 1-7 OF 7 REFERENCES

Edmonds polytopes and weakly hamiltonian graphs

- Mathematics, Computer ScienceMath. Program.
- 1973

A direct application of the linear programming duality theorem leads to a new necessary condition for the existence of hamiltonian circuits; this condition appears to be stronger than the ones previously known.

Depth-First Search and Linear Graph Algorithms

- Mathematics, Computer ScienceSIAM J. Comput.
- 1972

The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components…

Determinant Sums for Undirected Hamiltonicity

- Mathematics, Computer ScienceSIAM J. Comput.
- 2014

A Monte Carlo algorithm for Hamiltonicity detection in an $n$-vertex undirected graph running in O(1.657^{n}) time is presented, the first superpolynomial improvement on the worst case runtime for the problem since the O*(2^n) bound was established over 50 years ago.

A dynamic programming approach to sequencing problems

- Computer Science, MathematicsACM National Meeting
- 1961

A dynamic programming approach to the solution of three sequencing problems: a scheduling problem involving arbitrary cost functions, the traveling-salesman problem, and an assembly line balancing problem that admits of numerical solution through the use of a simple recursion scheme.

Zinc is not commercial, accessed: 2014-8-20

- 2014

Graph Theory, volume 173

- 2012