GRAPH MATROID AND ANALYSIS OF SLEEPING TREES IN A GRAPH

Authors

DOI:

https://doi.org/10.30890/2567-5273.2025-40-02-036

Keywords:

graph, matroid, spanning tree, Kruskal’s algorithm, graphic matroid, independent sets, combinatorial optimization

Abstract

This study explores the graphic matroid as a formal framework for modeling the construction of spanning trees in undirected graphs. By interpreting acyclic edge subsets as independent sets, the matroid structure provides a rigorous foundation for analyzin

References

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Oxley, J.G. (2006) Matroid Theory. Oxford: Oxford University Press. Available at: Oxford Academic (Accessed: 13 August 2025). https://academic.oup.com/book/34846

Wahlström, M. (2024). Representative set statements for delta-matroids and the Mader pp. 780–810. SIAM. Advance online publication. Available at: https://doi.org/10.1137/1.9781611977912

Koana, T. and Wahlström, M. (2025). Faster Algorithms on Linear Delta-Matroids. In: O. Beyersdorf, M. Pilipczuk, E. Pimentel, and N.K. Thắng, eds. 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics, vol. 327, article no. 62, pp. 62:1–62:19. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. Available at: https://drops.dagstuhl.de/storage/00lipics/lipics-vol327-stacs2025/LIPIcs.STACS.2025.62/LIPIcs.STACS.2025.62.pdf

Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to Algorithms (3rd ed.). MIT Press. Available at: Internet Archive (Accessed: 13 August 2025). https://archive.org/details/introduction-to-algorithms-third-edition-2009

Published

2025-08-30

How to Cite

Кулаковська, І. (2025). GRAPH MATROID AND ANALYSIS OF SLEEPING TREES IN A GRAPH. Modern Engineering and Innovative Technologies, 2(40-02), 21–31. https://doi.org/10.30890/2567-5273.2025-40-02-036

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