Geodesic
Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 825-836

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For the relaxation polyhedron $M(4,n)$ in the four-index axial assignment problem of order $n$, $n\geqslant 3$, a characterization of all possible types (except for a single case) of maximum noninteger vertices, i.e., vertices with $4n-3$ fractional components is proposed. A formula enumerating all the maximum noninteger vertices of the same type in $M(4,n)$ is derived. 
@article{ZVMMF_2013_53_5_a13,
     author = {V. M. Kravtsov and M. K. Kravtsov},
     title = {Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {825--836},
     publisher = {mathdoc},
     volume = {53},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a13/}
}
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V. M. Kravtsov; M. K. Kravtsov. Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 825-836. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a13/