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Beyond Quasi-Adjoint Graphs: On Polynomial-Time Solvable Cases of the Hamiltonian Cycle and Path Problems
Volume 35, Issue 4 (2024), pp. 807–816
Pub. online: 18 September 2024      Type: Research Article      Open accessOpen Access
Received
1 September 2023
Accepted
1 September 2024
Published
18 September 2024

Abstract

The Hamiltonian cycle and path problems are fundamental in graph theory and useful in modelling real-life problems. Research in this area is directed toward designing better and better algorithms for general problems, but also toward defining new special cases for which exact polynomial-time algorithms exist. In the paper, such new classes of digraphs are proposed. The classes include, among others, quasi-adjoint graphs, which are a superclass of adjoints, directed line graphs, and graphs modelling a DNA sequencing problem.

References

 
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Biographies

Kasprzak Marta
https://orcid.org/0000-0002-9863-5412
mkasprzak@cs.put.poznan.pl

M. Kasprzak is a professor at the Institute of Computing Science, Poznan University of Technology, Poland. She focuses her scientific research on bioinformatics, with a stress put on theoretical analysis of problems: combinatorial modelling of real-world problems, determining their computational complexity, designing algorithms. She published 73 articles and monographs, 43 of them indexed in Web of Science. She is a laureate of, among others, the Prime Minister Award for her doctoral dissertation, Award of the IV Division of Technical Sciences of the Polish Academy of Sciences in the field of computer science for her habilitation thesis, and the Medal of the National Education Commission.


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© 2024 Vilnius University
Open access article under the CC BY license.

Keywords
directed line graph quasi-adjoint graph Hamiltonian cycle Hamiltonian path

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