Abstract
Properties of nonegative matrices and algorithmic problems of combinatorics are considered in this survey, which is a continuation of a paper by the same authors. The bibliography covers primarily works published in Ref. Zh. Matematika from 1980 to 1983.
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Literature cited
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J. L. Brenner and E. T. H. Wang, “Permanental pairs of double stochastic matrices. II,” Linear Algebra Appl.,28, 39–41 (1979).
W. G. Bridges and R. A. Mena, “Rational circulants with rational spectra and cyclic strongly regular graphs,” Ars Combinatoria,8, 143–161 (1979).
R. A. Brualdi, “Matrices of 0's and 1's with total support,” J. Combin. Theory,A28, No. 3, 249–256 (1980).
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R. A. Brualdi and J. A. Ross, “Invariant sets for classes of matrices of zeros and ones,” Proc. Am. Math. Soc.,80, No. 4, 706–710 (1980).
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Toru Chiba, Ikuo Nishioka, and Isao Shirakawa, “An algorithm of maximal planarization of graphs,” Int. Symp. Circuits and Syst. Proc., Tokyo, 1979, New York, N. Y., s. a., pp. 649–652.
M. H. Clapp and R. C. Shiflett, “A Birkhoff theorem for doubly stochastic matrices with vector entries,” Stud. Appl. Math.,62, No. 3, 273–279 (1980).
C. J. Colbourn and M. J. Colbourn, “Deciding Hadamard equivalence of Hadamard matrices,” BIT (Sver.),21, No. 3, 374–376 (1981).
R. Cole and J. Hopcroft, “On edge coloring bipartite graphs,” SIAM J. Comput.,11, No. 3, 540–546 (1982).
D. Coppersmith and S. Winograd, “On the asymptotic complexity of matrix multiplication,” SIAM J. Comput.,11, No. 3, 472–492 (1982).
W. H. Cunningham and A. B. Marsh, III, “A primal algorithm for optimum matching,” Math. Program. Study,8, 50–72 (1978).
R. Dacic, “Common transversals of finite families,” Publ. Inst. Math.,26, 97–99 (1979).
D. De Caen and D. A. Gregory, “Prime Boolean matrices,” Lect. Notes Math.,829, 76–82 (1980).
M. Dehon, “Ranks of incidence matrices of (2, 3)-coverings,” Ars Combinatoria,9, 131–147 (1980).
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A. Farley, S. Hedetniemi, and A. Proskurowski, “Partitioning trees: matching, domination, and maximum diameter,” Int. J. Comput. Inf. Sci.,10, No. 1, 55–61 (1981).
W. Fernandez de la Vega and G. S. Lueker, “Bin packing can be solved within 1 + ε in linear time,” Combinatorica,1, No. 4, 349–355 (1981).
T. H. Foregger, “On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix,” Linear Algebra Appl.,32, Aug., 78–85 (1980).
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A. M. Frieze, “An algorithm for algebraic assignment problems,” Discrete Appl. Math.,1, No. 4, 253–259 (1979).
H. N. Gabow, “Using Euler partitions to edge color bipartite multigraphs,” Int. J. Comput. Inform. Sci.,5, No. 4, 245–255 (1976).
H. W. Gabow and G. Kariv, “Algorithms for edge coloring bipartite graphs,” Conf. Rec. 10 Annu. ACM symp. Theory Comput., San Diego, Calif., 1978, New York, N. Y. (1978), pp. 184–192.
A. M. Frieze and G. Kariv, “Algorithms for edge coloring bipartite graphs and multigraphs,” SIAM J. Comput.,11, No. 1, 117–129 (1982).
H. W. Gabow and E. W. Myers, “Finding all spanning trees of direct and undirected graphs,” ISAM J. Comput.,7, No. 3, 280–287 (1978).
M. R. Garey, R. L. Graham, D. S. Johnson, and D. E. Knuth, “Complexity results for bandwidth minimization,” SIAM J. Appl. Math.,34, No. 3, 477–495 (1978).
P. M. Gibson, “Generalized doubly stochastic and permutation matrices over a ring,” Linear Algebra Appl.,30, 101–107 (1980).
P. M. Gibson, “Permanental polytopes of doubly stochastic matrices,” Linear Algebra Appl.,32, Aug., 87–111 (1980).
V. Gligor and D. Maier, “Finding augmented-set bases,” SIAM J. Comput.,11, No. 3, 602–609 (1982).
T. Gonzales and J. Ja'Ja', “On the complexity of computing bilinear forms with {0, 1} constants,” J. Comput. Syst. Sci.,20, No. 1, 77–95 (1980).
A. Goralcikova and V. Koubek, “A reduct-and-closure algorithm for graphs,” Lect. Notes Comput. Sci.,74, 301–307 (1979).
D. Gouyou-Beauchamps, “The Hamiltonian circuit problem is polynomial for 4-connected planar graphs,” SIAM J. Comput.,11, No. 3, 529–539 (1982).
L. J. Gray and D. G. Wilson, “Nonnegative factorization of positive semidefinite nonnegative matrices,” Linear Algebra Appl.,31, 119–127 (1980).
R. D. Grone, D. G. Hoffman, and J. R. Wall, “Permutation matrix groups with positive sum,” Linear Algebra Appl., No. 45, 29–34 (1982).
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R. Hassin, “Maximum flow in (s, t) planar networks,” Inf. Process. Lett.,13, No. 3, 737 (1981).
P. Hell and D. G. Kirkpatrick, “Scheduling, matching, and coloring,” Alg. Methods Graph Theory, Vol. 1, Amsterdam; Budapest (1981), pp. 273–279.
Hirata Tomio, Akira Marouka, and Kimura Masayuki, “Efficient algorithm to solve the path cover problem for reducible flow graphs,” Int. Symp. Circuits Syst. Proc., Tokyo, 1979, New York, N. Y., s. a., pp. 637–640.
I. Holyer, “The NP-completeness of edge-coloring,” SIAM J. Comput.,10, No. 4, 718–720, (1981).
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Hsu Wen-Lian and G. L. Nemhauser, “Easy and hard bottleneck location problems,” Discrete Appl. Math.,1, No. 3, 209–215 (1979).
Hsu Wen-Lian and G. L. Nemhauser, “Algorithms for minimum covering by cliques and maximum clique in claw-free perfect graphs,” Discrete Math.,37, No. 2–3, 181–191 (1981).
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Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Mathematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 21, pp. 120–178, 1983.
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Nosov, V.A., Sachkov, V.N. & Tarakanov, V.E. Combinatorial analysis (nonnegative matrices, algorithmic problems). J Math Sci 29, 1051–1099 (1985). https://doi.org/10.1007/BF02104831
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DOI: https://doi.org/10.1007/BF02104831