Geodesic
Study of systems of equations over various classes of finite matroids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 1094-1102

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In the paper, it is proved that the problem of checking compatibility of a finite system of equations over a matroid of rank not exeeding $k$ is $\mathcal{NP}$-complete for ${k \geqslant 2}$. Moreover, it is proved that the problem of checking compatibility of a finite system of equations over a $k$-uniform matroid is also $\mathcal{NP}$-complete for ${k \geqslant 2}$, and the problem of checking compatibility of a finite system of equations over a partition matroid of rank not exeeding $k$ is polynomially solvable for ${k=2}$ and $\mathcal{NP}$-complete for ${k \geqslant 3}$.
Keywords: graph, matroid, system of equations, computational complexity. 
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     author = {A. V. Ilev},
     title = {Study of systems of equations over various classes of finite matroids},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1094--1102},
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     number = {2},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a16/}
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A. V. Ilev. Study of systems of equations over various classes of finite matroids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 1094-1102. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a16/