메뉴 건너뛰기




Volumn , Issue , 2007, Pages

Towards a Matroid-Minor Structure Theory

Author keywords

Graphs minor project; Matroids; Rota's conjecture

Indexed keywords


EID: 84920751479     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780198571278.003.0005     Document Type: Chapter
Times cited : (20)

References (33)
  • 1
    • 0346321988 scopus 로고
    • On Reid's characterization of the ternary matroids
    • R. E. Bixby, On Reid's characterization of the ternary matroids, J. Combin. Theory Ser. B 26 (1979) 174-204.
    • (1979) J. Combin. Theory Ser. B , vol.26 , pp. 174-204
    • Bixby, R.E.1
  • 2
    • 1842565335 scopus 로고
    • A min-max theorem using matroid separations
    • Seattle WA, Contemp. Math. 197 Amer. Math. Soc., Providence RI
    • J. Dharmatilake, A min-max theorem using matroid separations, Matroid Theory (Seattle WA 1995) 333-342, Contemp. Math. 197 Amer. Math. Soc., Providence RI (1996).
    • (1995) Matroid Theory , pp. 333-342
    • Dharmatilake, J.1
  • 4
    • 0002681234 scopus 로고
    • A class of geometric lattices based on finite groups
    • T. Dowling, A class of geometric lattices based on finite groups, J. Combin. Theory Ser. B 14 (1973) 61-86.
    • (1973) J. Combin. Theory Ser. B , vol.14 , pp. 61-86
    • Dowling, T.1
  • 5
  • 8
    • 0036211275 scopus 로고    scopus 로고
    • Branch-width and well-quasiordering in matroids and graphs
    • J. Geelen, A. M. H. Gerards, and G. Whittle, Branch-width and well-quasiordering in matroids and graphs, J. Combin. Theory Ser. B 84 (2002) 270-290.
    • (2002) J. Combin. Theory Ser. B , vol.84 , pp. 270-290
    • Geelen, J.1    Gerards, A.M.H.2    Whittle, G.3
  • 11
    • 33645900864 scopus 로고    scopus 로고
    • On Rota's Conjecture and excluded minors containing large projective geometries, to appear
    • J. Geelen, B. Gerards, and G. Whittle, On Rota's Conjecture and excluded minors containing large projective geometries, to appear in J. Combin. Theory Ser. B 96 (2006) 405-525.
    • (2006) J. Combin. Theory Ser. B , vol.96 , pp. 405-525
    • Geelen, J.1    Gerards, B.2    Whittle, G.3
  • 12
    • 23244439890 scopus 로고    scopus 로고
    • Excluding a planar graph from GF(q)-representable matroids
    • submitted
    • J. Geelen, B. Gerards, and G. Whittle, Excluding a planar graph from GF(q)-representable matroids, submitted.
    • Geelen, J.1    Gerards, B.2    Whittle, G.3
  • 13
    • 21844458779 scopus 로고    scopus 로고
    • Inequivalent representations of matroids I: An overview
    • in preparation
    • J. Geelen, B. Gerards, and G. Whittle, Inequivalent representations of matroids I: An overview, in preparation.
    • Geelen, J.1    Gerards, B.2    Whittle, G.3
  • 14
  • 15
    • 0037374628 scopus 로고    scopus 로고
    • Cliques in dense GF(q)-representable matroids
    • J. Geelen and G. Whittle, Cliques in dense GF(q)-representable matroids, J. Combin. Theory Ser. B 87 (2003) 264-269.
    • (2003) J. Combin. Theory Ser. B , vol.87 , pp. 264-269
    • Geelen, J.1    Whittle, G.2
  • 16
    • 84919557734 scopus 로고    scopus 로고
    • Branch-width, parse trees, and monadic second-order logic for matroids
    • preprint, Extended abstract in STACS
    • P. Hliněný, Branch-width, parse trees, and monadic second-order logic for matroids, preprint, Extended abstract in STACS 2003.
    • (2003)
    • Hliněný, P.1
  • 18
    • 84878056912 scopus 로고    scopus 로고
    • Connectivity in binary matroids
    • Handwritten manuscript
    • T. Johnson, N. Robertson, and P. D. Seymour, Connectivity in binary matroids, Handwritten manuscript.
    • Johnson, T.1    Robertson, N.2    Seymour, P.D.3
  • 19
    • 84963024014 scopus 로고
    • The representation problem for independence functions
    • T. Lazarson, The representation problem for independence functions, J. London Math. Soc. 33 (1958) 21-25.
    • (1958) J. London Math. Soc. , vol.33 , pp. 21-25
    • Lazarson, T.1
  • 20
    • 0030187155 scopus 로고    scopus 로고
    • On inequivalent representations of matroids over finite fields
    • J. G. Oxley, D. L. Vertigan, and G. P. Whittle, On inequivalent representations of matroids over finite fields, J. Combin. Theory Ser. B 67 (1996) 325-343.
    • (1996) J. Combin. Theory Ser. B , vol.67 , pp. 325-343
    • Oxley, J.G.1    Vertigan, D.L.2    Whittle, G.P.3
  • 21
    • 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
  • 22
  • 23
    • 0001227241 scopus 로고
    • Graph minors. X. Obstructions to tree decomposition
    • N. Robertson and P. D. Seymour, Graph minors. X. Obstructions to tree decomposition, J. Combin. Theory Ser. B 52 (1991) 153-190.
    • (1991) J. Combin. Theory Ser. B , vol.52 , pp. 153-190
    • Robertson, N.1    Seymour, P.D.2
  • 24
    • 0002848005 scopus 로고
    • Graph minors. X111. The disjoint paths problem
    • N. Robertson and P. D. Seymour, Graph minors. X111. The disjoint paths problem, J. Combin. Theory Ser. B 63 (1995) 65-110.
    • (1995) J. Combin. Theory Ser. B , vol.63 , pp. 65-110
    • Robertson, N.1    Seymour, P.D.2
  • 27
    • 0011518480 scopus 로고
    • Combinatorial theory, old and new
    • (Nice, Sept. 1970) Gauthier-Chichester
    • G.-C. Rota, Combinatorial theory, old and new, in Proc. Internat. Cong. Math. (Nice, Sept. 1970) Gauthier-Chichester (1970) pp. 229-233.
    • (1970) Proc. Internat. Cong. Math. , pp. 229-233
    • Rota, G.-C.1
  • 28
    • 0001523212 scopus 로고
    • Matroid representation over GF(3)
    • P. D. Seymour, Matroid representation over GF(3), J. Combin. Theory Ser. B 26 (1979) 159-173.
    • (1979) J. Combin. Theory Ser. B , vol.26 , pp. 159-173
    • Seymour, P.D.1
  • 29
    • 84968508683 scopus 로고
    • A homotopy theorem for matroids, I, II
    • W. T. Tutte, A homotopy theorem for matroids, I, II, Trans. Amer. Math. Soc. 88 (1958) 144-174.
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 144-174
    • Tutte, W.T.1
  • 31
    • 0008388595 scopus 로고    scopus 로고
    • Stabilizers of classes of representable matroids
    • G. P. Whittle, Stabilizers of classes of representable matroids, J. Combin. Theory Ser. B 77 (1999) 39-72.
    • (1999) J. Combin. Theory Ser. B , vol.77 , pp. 39-72
    • Whittle, G.P.1
  • 32
    • 0002766745 scopus 로고
    • Biased graphs. II. The three matroids
    • T. Zaslavsky, Biased graphs. II. The three matroids, J. Combin. Theory Ser. B 51 (1991) 46-72.
    • (1991) J. Combin. Theory Ser. B , vol.51 , pp. 46-72
    • Zaslavsky, T.1
  • 33
    • 15544389538 scopus 로고    scopus 로고
    • A mathematical bibliography of signed and gain graphs and allied areas. Manuscript prepared with Marge Pratt
    • Dynamic Surveys, electronic
    • T. Zaslavsky, A mathematical bibliography of signed and gain graphs and allied areas. Manuscript prepared with Marge Pratt. Electron. J. Combin. 5 (1998) Dynamic Surveys, pp. 8, 124 (electronic).
    • (1998) Electron. J. Combin , vol.5 , pp. 8+124
    • Zaslavsky, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.