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Volumn 109, Issue 3, 1998, Pages 672-685

The line index and minimum cut of weighted graphs

Author keywords

Balanced graph; Line index; Minimum cut; Planar graph; Series parallel graph; Weighted graph

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS;

EID: 0347659166     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(97)00196-3     Document Type: Article
Times cited : (10)

References (23)
  • 1
    • 0001368104 scopus 로고
    • Topology of series-parallel networks
    • R.J. Duffin, Topology of series-parallel networks, J. Math. Analysis Appl. 10 (1965) 303-318.
    • (1965) J. Math. Analysis Appl. , vol.10 , pp. 303-318
    • Duffin, R.J.1
  • 3
    • 0025433817 scopus 로고
    • Unifying maximum cut and minimum cut of a planar graph
    • W.K. Shih, S. Wu, Y.S. Kuo, Unifying maximum cut and minimum cut of a planar graph, IEEE Trans. Comput. 39 (1990) 694-697.
    • (1990) IEEE Trans. Comput. , vol.39 , pp. 694-697
    • Shih, W.K.1    Wu, S.2    Kuo, Y.S.3
  • 4
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • R.E. Miller, J.W. Thatcher (Eds.), Plenum Press, New York
    • R.M. Karp, Reducibility among combinatorial problems, in: R.E. Miller, J.W. Thatcher (Eds.), Complexity of Computer Computations, Plenum Press, New York, 1972.
    • (1972) Complexity of Computer Computations
    • Karp, R.M.1
  • 6
    • 0002068485 scopus 로고
    • Finding the maximum cut in a graph
    • G.I. Orlova, Y.G. Dorfman, Finding the maximum cut in a graph, Engrg. Cybernetics 10 (1972) 502-504.
    • (1972) Engrg. Cybernetics , vol.10 , pp. 502-504
    • Orlova, G.I.1    Dorfman, Y.G.2
  • 7
    • 0000120312 scopus 로고
    • Finding a maximum cut of a planar graph in polynomial time
    • F.O. Hadlock, Finding a maximum cut of a planar graph in polynomial time, SIAM J. Comput. 4 (1975) 221-225.
    • (1975) SIAM J. Comput. , vol.4 , pp. 221-225
    • Hadlock, F.O.1
  • 8
    • 0346146448 scopus 로고
    • NP-completeness of maximum-cut and cycle-covering problems for a planar graph
    • A.P. Terebenkov, NP-completeness of maximum-cut and cycle-covering problems for a planar graph, Cybernetics 27 (1991) 16-20.
    • (1991) Cybernetics , vol.27 , pp. 16-20
    • Terebenkov, A.P.1
  • 9
    • 0019627062 scopus 로고
    • Weakly bipartite graphs and the max-cut problem
    • M. Grötschel, W.R. Pulleyblank, Weakly bipartite graphs and the max-cut problem, Oper. Res. Letters 1 (1981) 23-27.
    • (1981) Oper. Res. Letters , vol.1 , pp. 23-27
    • Grötschel, M.1    Pulleyblank, W.R.2
  • 10
    • 0011588477 scopus 로고
    • Maximum cuts and large bipartite subgraphs, Combinatorial Optimization, DIMACS ser
    • S. Poljak, Z. Tuza, Maximum cuts and large bipartite subgraphs, Combinatorial Optimization, DIMACS ser. in Discrete Mathematics and Theoretical Computer Science 20 (1995) 181-244.
    • (1995) Discrete Mathematics and Theoretical Computer Science , vol.20 , pp. 181-244
    • Poljak, S.1    Tuza, Z.2
  • 11
    • 0000989134 scopus 로고
    • On the notion of balance of a signed graph
    • F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1954) 143-146.
    • (1954) Michigan Math. J. , vol.2 , pp. 143-146
    • Harary, F.1
  • 12
    • 84925923678 scopus 로고
    • A simple algorithm to detect balance in signed graphs
    • F. Harary, J.A. Kabell, A simple algorithm to detect balance in signed graphs, Mathematical Social Sciences 1 (1980) 131-136.
    • (1980) Mathematical Social Sciences , vol.1 , pp. 131-136
    • Harary, F.1    Kabell, J.A.2
  • 13
    • 0348038165 scopus 로고
    • An algorithm for identifying Morishima and anti-Morishima matrices and balanced digraphs
    • J.S. Maybee, S.J. Maybee, An algorithm for identifying Morishima and anti-Morishima matrices and balanced digraphs, Mathematical Social Sciences 6 (1983) 99-103.
    • (1983) Mathematical Social Sciences , vol.6 , pp. 99-103
    • Maybee, J.S.1    Maybee, S.J.2
  • 14
    • 0347407209 scopus 로고
    • Computing the line index of balance of signed outer-planar graphs
    • A.M. Farley, A. Proskurowski, Computing the line index of balance of signed outer-planar graphs, Congressus Numerantium 32 (1981) 323-332.
    • (1981) Congressus Numerantium , vol.32 , pp. 323-332
    • Farley, A.M.1    Proskurowski, A.2
  • 15
    • 0001261128 scopus 로고
    • Maximal flow through a network
    • C. Ford, D. Fulkerson, Maximal flow through a network, Canad. J. Math. 8 (1956) 399-404.
    • (1956) Canad. J. Math. , vol.8 , pp. 399-404
    • Ford, C.1    Fulkerson, D.2
  • 17
    • 51249166833 scopus 로고
    • On some extremal problems in graph theory
    • P. Erdös, On some extremal problems in graph theory, Isarel J. Math. 3 (1965) 113-116.
    • (1965) Isarel J. Math. , vol.3 , pp. 113-116
    • Erdös, P.1
  • 19
    • 0346776717 scopus 로고
    • Comments on F. Hadlock's paper: Finding a maximum cut of a planar graph in polynomial time
    • K. Aoshima, M. Iri, Comments on F. Hadlock's paper: Finding a maximum cut of a planar graph in polynomial time, SIAM J. Comput. 6 (1977) 86-87.
    • (1977) SIAM J. Comput. , vol.6 , pp. 86-87
    • Aoshima, K.1    Iri, M.2
  • 20
    • 0042456012 scopus 로고
    • The max-cut problem and quadratic 0-1 optimization; polyhedral aspects, relaxations and bounds
    • E. Boros, P.L. Hammer, The max-cut problem and quadratic 0-1 optimization; polyhedral aspects, relaxations and bounds, Annals of Operations Research 33 (1991) 151-180.
    • (1991) Annals of Operations Research , vol.33 , pp. 151-180
    • Boros, E.1    Hammer, P.L.2
  • 22
    • 84909571832 scopus 로고
    • A polynomial algorithm for the max-cut problem of graphs without long odd cycles
    • Universität Bonn
    • M. Grötschel, G.L. Nemhauser, A polynomial algorithm for the max-cut problem of graphs without long odd cycles, Report No. 8221-OR, Universität Bonn, 1982.
    • (1982) Report No. 8221-OR
    • Grötschel, M.1    Nemhauser, G.L.2
  • 23
    • 0003780715 scopus 로고
    • Addison-Wesley, Reading, MA
    • F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
    • (1969) Graph Theory
    • Harary, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.