메뉴 건너뛰기




Volumn , Issue , 2007, Pages

Complexity of Graph Polynomials

Author keywords

Graph polynomials; Graphs; Matroids; Polynomial time algorithms; Tutte polynomial

Indexed keywords


EID: 84920753205     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780198571278.003.0013     Document Type: Chapter
Times cited : (2)

References (51)
  • 2
    • 0001919985 scopus 로고    scopus 로고
    • A polynomial-time algorithm for computation of the Tutte polynomials of graphs of bounded treewidth
    • A. Andrzejak, A polynomial-time algorithm for computation of the Tutte polynomials of graphs of bounded treewidth, Discrete Mathematics 190 (1998) 39-54.
    • (1998) Discrete Mathematics , vol.190 , pp. 39-54
    • Andrzejak, A.1
  • 3
    • 0012817597 scopus 로고
    • The complexities of the coefficients of the Tutte polynomial
    • J. D. Annan, The complexities of the coefficients of the Tutte polynomial, Discrete Applied Mathematics 57 (1995) 93-103.
    • (1995) Discrete Applied Mathematics , vol.57 , pp. 93-103
    • Annan, J.D.1
  • 5
    • 0002003951 scopus 로고
    • Linear time algorithms for NP-hard problems restricted to partial -trees
    • S. Arnborg and A. Proskurowski, Linear time algorithms for NP-hard problems restricted to partial -trees, Discrete Applied Mathematics 23 (1989) 11-24.
    • (1989) Discrete Applied Mathematics , vol.23 , pp. 11-24
    • Arnborg, S.1    Proskurowski, A.2
  • 6
    • 85037918238 scopus 로고
    • A tourist guide through treewidth
    • H. L. Bodlaender, A tourist guide through treewidth, Acta Cybernetica 11 (1993) 1-21.
    • (1993) Acta Cybernetica , vol.11 , pp. 1-21
    • Bodlaender, H.L.1
  • 7
    • 0001294529 scopus 로고    scopus 로고
    • A linear time algorithm for finding tree-decompositions of small treewidth
    • H. L. Bodlaender, A linear time algorithm for finding tree-decompositions of small treewidth, SIAM Journal on Computing, 25, (1996) 1305-1317.
    • (1996) SIAM Journal on Computing , vol.25 , pp. 1305-1317
    • Bodlaender, H.L.1
  • 8
    • 0001755174 scopus 로고
    • The Tutte polynomial
    • (A. Barlotti ed.), Naples, CIME: Liguori editore
    • T. H. Brylawski, The Tutte polynomial, in Matroid Theory and its Applications (A. Barlotti ed.), Naples, CIME: Liguori editore (1982) pp. 125-275.
    • (1982) Matroid Theory and its Applications , pp. 125-275
    • Brylawski, T.H.1
  • 9
    • 0002127159 scopus 로고
    • The Tutte polynomial and its applications
    • (N. White ed.), Cambridge University Press, Cambridge
    • T. H. Brylawski and J. G. Oxley, The Tutte polynomial and its applications, in Matroid applications (N. White ed.), Cambridge University Press, Cambridge (1992) pp. 123-225.
    • (1992) Matroid applications , pp. 123-225
    • Brylawski, T.H.1    Oxley, J.G.2
  • 10
    • 51249163854 scopus 로고
    • The complexity of computing the Tutte polynomial on transversal matroids
    • C. J. Colbourn, J. S. Provan, and D. Vertigan, The complexity of computing the Tutte polynomial on transversal matroids, Combinatorica 15 (1995) 1-10.
    • (1995) Combinatorica , vol.15 , pp. 1-10
    • Colbourn, C.J.1    Provan, J.S.2    Vertigan, D.3
  • 12
    • 33645682335 scopus 로고    scopus 로고
    • The complexity of counting colourings of subgraphs of the grid
    • G. E. Farr, The complexity of counting colourings of subgraphs of the grid, Combin. Probab. Comput. 15 (2006) 377-383.
    • (2006) Combin. Probab. Comput. , vol.15 , pp. 377-383
    • Farr, G.E.1
  • 13
    • 0040713233 scopus 로고
    • A correlation inequality involving stable sets and chromatic polynomials
    • G. E. Farr, A correlation inequality involving stable sets and chromatic polynomials, J. Combin. Theory Ser. B, 58 (1993) 14-21.
    • (1993) J. Combin. Theory Ser. B , vol.58 , pp. 14-21
    • Farr, G.E.1
  • 14
    • 0000476184 scopus 로고
    • On a general class of graph polynomials
    • E. J. Farrell, On a general class of graph polynomials, J. Combin. Theory Ser. B 26 (1979) 111-122.
    • (1979) J. Combin. Theory Ser. B , vol.26 , pp. 111-122
    • Farrell, E.J.1
  • 15
    • 0011027803 scopus 로고
    • On the dimer solution of planar Ising models
    • M. E. Fisher, On the dimer solution of planar Ising models, Journal of Mathematical Physics 7 (1966) 1776-1781.
    • (1966) Journal of Mathematical Physics , vol.7 , pp. 1776-1781
    • Fisher, M.E.1
  • 17
    • 33645657538 scopus 로고    scopus 로고
    • On the complexity of computing the Tutte polynomial of bicircular matroids
    • O. Giménez and M. Noy, On the complexity of computing the Tutte polynomial of bicircular matroids, Combin. Probab. Comput. 15 (2006) 385-395.
    • (2006) Combin. Probab. Comput. , vol.15 , pp. 385-395
    • Giménez, O.1    Noy, M.2
  • 19
    • 33645667803 scopus 로고    scopus 로고
    • The Tutte polynomial for matroids of bounded branch-width
    • P. Hliněný, The Tutte polynomial for matroids of bounded branch-width, Combin. Probab. Comput. 15 (2006) 397-409.
    • (2006) Combin. Probab. Comput. , vol.15 , pp. 397-409
    • Hliněný, P.1
  • 21
    • 0009002383 scopus 로고
    • 2-dimensional monomer-dimer systems are computationally intractable
    • M. R. Jerrum, 2-dimensional monomer-dimer systems are computationally intractable, Journal of Statistical Physics 48 (1987) 121-134.
    • (1987) Journal of Statistical Physics , vol.48 , pp. 121-134
    • Jerrum, M.R.1
  • 22
    • 84919549747 scopus 로고    scopus 로고
    • Private communication
    • M. R. Jerrum, Private communication (2005).
    • (2005)
    • Jerrum, M.R.1
  • 23
    • 0001834352 scopus 로고
    • Graph theory and crystal physics
    • Academic Press, London
    • P. W. Kasteleyn, Graph theory and crystal physics, in Graph Theory and Theoretical Physics, Academic Press, London (1967) pp. 43-110.
    • (1967) Graph Theory and Theoretical Physics , pp. 43-110
    • Kasteleyn, P.W.1
  • 24
    • 0141904913 scopus 로고
    • The asymptotic number of geometries
    • D. E. Knuth, The asymptotic number of geometries, J. Combin. Theory Ser. A 17 (1974) 398-401.
    • (1974) J. Combin. Theory Ser. A , vol.17 , pp. 398-401
    • Knuth, D.E.1
  • 25
  • 26
    • 8344269316 scopus 로고    scopus 로고
    • Coloured Tutte polynomials and Kaufmann brackets for graphs of bounded tree width
    • J. A. Makowsky, Coloured Tutte polynomials and Kaufmann brackets for graphs of bounded tree width, Discrete Applied Mathematics 145 (2005) 276-290.
    • (2005) Discrete Applied Mathematics , vol.145 , pp. 276-290
    • Makowsky, J.A.1
  • 27
    • 0038404859 scopus 로고    scopus 로고
    • Farrell polynomials on graphs of bounded tree width
    • Special issue of FPSAC'01 papers
    • J. A. Makowsky, and J. P. Mariño, Farrell polynomials on graphs of bounded tree width, Advances in Applied Mathematics 30 (2003) 160-176, Special issue of FPSAC'01 papers.
    • (2003) Advances in Applied Mathematics , vol.30 , pp. 160-176
    • Makowsky, J.A.1    Mariño, J.P.2
  • 28
    • 33645698404 scopus 로고    scopus 로고
    • Evaluating a weighted graph polynomial for graphs of bounded tree-width
    • Submitted
    • S. D. Noble, Evaluating a weighted graph polynomial for graphs of bounded tree-width, Submitted.
    • Noble, S.D.1
  • 30
    • 0032262138 scopus 로고    scopus 로고
    • Evaluating the Tutte polynomial for graphs of bounded treewidth
    • S. D. Noble, Evaluating the Tutte polynomial for graphs of bounded treewidth, Combinatorics, Probability and Computing 7. (1998) 307-321.
    • (1998) Combinatorics, Probability and Computing , vol.7 , pp. 307-321
    • Noble, S.D.1
  • 31
    • 33645670799 scopus 로고    scopus 로고
    • Evaluating the rank generating function of a graphic - polymatroid
    • S. D. Noble, Evaluating the rank generating function of a graphic - polymatroid, Combin. Probab. Comput. 15 (2006) 449-461.
    • (2006) Combin. Probab. Comput. , vol.15 , pp. 449-461
    • Noble, S.D.1
  • 32
    • 0040118794 scopus 로고    scopus 로고
    • A weighted graph polynomial from Vassiliev invariants
    • S. D. Noble, and D. J. A. Welsh, A weighted graph polynomial from Vassiliev invariants, Annales de l'institut Fourier 49 (1999) 1057-1087.
    • (1999) Annales de l'institut Fourier , vol.49 , pp. 1057-1087
    • Noble, S.D.1    Welsh, D.J.A.2
  • 33
    • 0004061262 scopus 로고
    • Number 3 in Oxford Graduate Texts in Mathematics, Oxford University Press, Oxford
    • J. G. Oxley, Matroid Theory, Number 3 in Oxford Graduate Texts in Mathematics, Oxford University Press, Oxford (1992) .
    • (1992) Matroid Theory
    • Oxley, J.G.1
  • 34
    • 38249010667 scopus 로고
    • Tutte polynomials computable in polynomial time
    • J. G. Oxley and D. J. A. Welsh, Tutte polynomials computable in polynomial time, Discrete Mathematics 109 (1992) 185-192.
    • (1992) Discrete Mathematics , vol.109 , pp. 185-192
    • Oxley, J.G.1    Welsh, D.J.A.2
  • 35
    • 0038580929 scopus 로고
    • Tutte invariants for 2- polymatroids
    • (N. Robertson and P. D. Seymour, eds.), Number 147 in Contemporary Mathematics, AMS
    • J. G. Oxley, and G. P. Whittle, Tutte invariants for 2- polymatroids, in Graph Structure Theory (N. Robertson and P. D. Seymour, eds.), Number 147 in Contemporary Mathematics (1993) pp. 9-19. AMS.
    • (1993) Graph Structure Theory , pp. 9-19
    • Oxley, J.G.1    Whittle, G.P.2
  • 37
    • 0000166629 scopus 로고
    • The complexity of counting cuts and of computing the probability that a graph is connected
    • J. S. Provan, and M. O. Ball, The complexity of counting cuts and of computing the probability that a graph is connected, SIAM Journal on Computing 12 (1983) 777-788.
    • (1983) SIAM Journal on Computing , vol.12 , pp. 777-788
    • Provan, J.S.1    Ball, M.O.2
  • 38
    • 0000673493 scopus 로고
    • Graph minors II. Algorithmic aspects of tree-width
    • N. Robertson and P. D. Seymour, Graph minors II. Algorithmic aspects of tree-width. Journal of Algorithms 7 (1986) 309-322.
    • (1986) Journal of Algorithms , vol.7 , pp. 309-322
    • Robertson, N.1    Seymour, P.D.2
  • 39
    • 3042806238 scopus 로고
    • Graph minors IV. Tree-width and wellquasi- ordering
    • N. Robertson, and P. D. Seymour, Graph minors IV. Tree-width and wellquasi- ordering, J. Combin. Theory Ser. B 48 (1990) 227-254.
    • (1990) J. Combin. Theory Ser. B , vol.48 , pp. 227-254
    • Robertson, N.1    Seymour, P.D.2
  • 40
    • 0002227937 scopus 로고
    • On the principal edge tripartition of a graph
    • P. Rosenstiehl, and R. C. Read, On the principal edge tripartition of a graph, Ann Discrete Math. 3 (1978) 195-226.
    • (1978) Ann Discrete Math. , vol.3 , pp. 195-226
    • Rosenstiehl, P.1    Read, R.C.2
  • 41
    • 29844450023 scopus 로고    scopus 로고
    • The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
    • Surveys in Combinatorics, 2005 (B. S. Webb, ed.), Volume, Cambridge University Press, Cambridge
    • A. D. Sokal, The multivariate Tutte polynomial (alias Potts model) for graphs and matroids, in Surveys in Combinatorics, 2005 (B. S. Webb, ed.), Volume 327 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (2005).
    • (2005) London Mathematical Society Lecture Note Series , vol.327
    • Sokal, A.D.1
  • 42
    • 33644772216 scopus 로고    scopus 로고
    • On the colored Tutte polynomial of a graph of bounded treewidth
    • L. Traldi, On the colored Tutte polynomial of a graph of bounded treewidth, Discrete Appl. Math. 154 (2006) 1032-1036.
    • (2006) Discrete Appl. Math. , vol.154 , pp. 1032-1036
    • Traldi, L.1
  • 43
    • 0002092950 scopus 로고
    • A contribution to the theory of chromatic polynomials
    • W. T. Tutte, A contribution to the theory of chromatic polynomials. Canad. J. Math. 6 (1954) 80-91.
    • (1954) Canad. J. Math. , vol.6 , pp. 80-91
    • Tutte, W.T.1
  • 44
    • 49249151236 scopus 로고
    • The complexity of computing the permanent
    • L. G. Valiant, The complexity of computing the permanent, Theoretical Computer Science 8 (1979) 189-201.
    • (1979) Theoretical Computer Science , vol.8 , pp. 189-201
    • Valiant, L.G.1
  • 45
    • 33745464366 scopus 로고    scopus 로고
    • The computational complexity of Tutte invariants for cubic planar graphs
    • Unpublished manuscript
    • D. Vertigan, The computational complexity of Tutte invariants for cubic planar graphs, Unpublished manuscript.
    • Vertigan, D.1
  • 46
    • 33745454767 scopus 로고    scopus 로고
    • The computational complexity of Tutte invariants for planar graphs
    • D. Vertigan, The computational complexity of Tutte invariants for planar graphs, SIAM Journal of Computing 35 (2006) 690-712.
    • (2006) SIAM Journal of Computing , vol.35 , pp. 690-712
    • Vertigan, D.1
  • 47
    • 0038901795 scopus 로고    scopus 로고
    • Bicycle dimension and special points of the Tutte polynomial
    • D. Vertigan, Bicycle dimension and special points of the Tutte polynomial, J. Combinatorial Theory Ser. B 74 (1998) 378-396.
    • (1998) J. Combinatorial Theory Ser. B , vol.74 , pp. 378-396
    • Vertigan, D.1
  • 49
    • 84971698102 scopus 로고
    • The computational complexity of the Tutte plane: the bipartite case
    • D. L. Vertigan, and D. J. A. Welsh, The computational complexity of the Tutte plane: the bipartite case, Combinatorics Probability and Computing 1 (1992) 181-187.
    • (1992) Combinatorics Probability and Computing , vol.1 , pp. 181-187
    • Vertigan, D.L.1    Welsh, D.J.A.2
  • 50
    • 0004045430 scopus 로고
    • Number 8 in London Mathematical Society Monographs, Academic Press
    • D. J. A. Welsh, Matroid Theory, Number 8 in London Mathematical Society Monographs, Academic Press (1976).
    • (1976) Matroid Theory
    • Welsh, D.J.A.1
  • 51
    • 0003518588 scopus 로고
    • Number 186 in London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge
    • D. J. A. Welsh, Complexity : Knots, Colourings, and Counting, Number 186 in London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (1993).
    • (1993) Complexity : Knots, Colourings, and Counting
    • Welsh, D.J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.