Geodesic
A win-win algorithm for~the~$(k+1)$-LST/$k$-pathwidth~problem
Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 4, pp. 117-124.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe a win-win algorithm that produces in polynomial of size of a graph $G$ and given parameter $k$ time either a spanning tree with al least $k+1$ leaves or a path decomposition with width at most $k$. This algorithm is optimal due to the path decomposition theorem [1]. Bibliogr. 5.
Keywords: path decomposition, spanning tree, $k$-LST problem, win-win algorithm
Mots-clés : FPT. 
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A. G. Klyuchikov; M. N. Vyalyi. A win-win algorithm for~the~$(k+1)$-LST/$k$-pathwidth~problem. Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 4, pp. 117-124. http://geodesic.mathdoc.fr/item/DA_2021_28_4_a4/

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[2] Douglas R. J., “NP-completeness and degree restricted spanning trees”, Discrete Math., 105:1-3 (1992), 41–47 | DOI | Zbl

[3] Kashiwabara T., Fujisawa T., “NP-completeness of the problem of finding a minimum-clique-number interval graph containing a given graph as a subgraph”, Proc. Int. Symp. Circuits and Systems (Tokyo, Japan, July 17–19, 1979), IEEE, New York, 1979, 657–660

[4] Bodlaender H. L., Demaine E. D., Fellows M. R. et al., Open problems in parameterized and exact computation — IWPEC 2008, Technical Report UU-CS-2008-017, Utrecht Univ., Utrecht, 2008 (accessed Aug. 3, 2021) http://www.cs.uu.nl/research/techreps/repo/CS-2008/2008-017.pdf

[5] Diestel R., “Graph minors I: A short proof of the path-width theorem”, Comb. Prob. Comput., 4:1 (1995), 27–30 | DOI | Zbl