List of Publications

 

 

Martin Kochol (2012)

 

 

  1. M. Kochol: Construction of crossing-critical graphs, Discrete Mathematics, vol. 66 (1987), pp. 311–313.
  2. M. Kochol: Generalized Pascal triangles with maximal left periods, Computers and Artificial Intelligence, vol. 6 (1987), pp. 59–70.
  3. M. Kochol: Efficient monotone circuit for threshold functions, Information Processing Lettres, vol. 32 (1989), pp. 121–122.
  4. M. Kochol: Latin (n x n x (n — 2))-parallelepipeds not completing to a latin cube, Mathematica Slovaca, vol. 39 (1989), pp. 121–125.
  5. M. Kochol: Varieties of modular p-algebras not containing M3,3, Algebra Universalis, vol. 28 (1991), pp. 559–588.
  6. M. Kochol: Latin parallelepipeds not completing to a latin cube, Mathematica Slovaca, vol. 41 (1991), pp. 3–9.
  7. M. Kochol: Linear jump of crossing number for non Kuratowski edge of a graph, Radovi Mathematički, vol. 7 (1991), pp. 177–184.
  8. M. Kochol: The notion and basic properties of M-transversals, Discrete Mathematics, vol. 104 (1992), pp. 191–196.
  9. M. Kochol: A note on the arboricity of graphs, Graphs and Combinatorics, vol. 8 (1992), pp. 313–315.
  10. M. Kochol: Constructive approximation of a ball by polytopes, Mathematica Slovaca, vol. 44 (1994), pp. 99–105.
  11. M. Kochol: About a generalization of transversals, Mathematica Bohemica, vol. 119 (1994), pp. 143–149.
  12. M. Kochol: Compatible systems of representatives, Discrete Mathematics, vol. 132 (1994), pp. 115–126.
  13. A. Huck and M. Kochol: Five cycle double covers of some cubic graphs, Journal of Combinatorial Theory Series B, vol. 64 (1995), pp. 119–125.
  14. M. Kochol: Quasi polymatroidal flow networks, Acta Mathematica Universitatis Comenianae (New Series), vol. 64 (1995), pp. 83–97.
  15. M. Kochol: Relatively narrow latin parallelepipeds that cannot be extended to a latin cube, Ars Combinatoria, vol. 40 (1995), pp. 247–260.
  16. M. Kochol: Symmetrized and continuous generalization of transversals, Mathematica Bohemica, vol. 121 (1996), pp. 95–106.
  17. M. Kochol: Snarks without small cycles, Journal of Combinatorial Theory Series B, vol. 67 (1996), pp. 34–47.
  18. M. Kochol: A cyclically 6-edge-connected snark of order 118, Discrete Mathematics, vol. 161 (1996), pp. 297–300.
  19. M. Kochol: Hypothetical complexity of the nowhere-zero 5-flow problem, Journal of Graph Theory, vol. 28 (1998), pp. 1–11.
  20. M. Kochol: Partial intersection theorem and flows in abstract networks, SIAM Journal on Discrete Mathematics, vol. 11 (1998), pp. 468–486.
  21. M. Kochol: An elementary proof of the fundamental theorem of algebra, International Journal of Mathematical Education in Science and Technology, vol. 30 (1999), pp. 614–615.
  22. M. Kochol: Cubic graphs without a Petersen minor have nowhere-zero 5-flows, Acta Mathematica Universitatis Comenianae (New Series), vol. 68 (1999), pp. 249–252.
  23. M. Kochol: Equivalence of Fleischner’s and Thomassen’s conjectures, Journal of Combinatorial Theory Series B, vol. 78 (2000), pp. 277–279.
  24. M. Kochol: Stable dominating circuits in snarks, Discrete Mathematics, vol. 233 (2001), pp. 247–256.
  25. M. Kochol: An equivalent version of the 3-flow conjecture, Journal of Combinatorial Theory Series B, vol. 83 (2001), pp. 258–261.
  26. M. Kochol: Superposition and constructions of graphs without nowhere-zero k-flows, European Journal of Combinatorics, vol. 23 (2002), pp. 281–306.
  27. M. Kochol: Polynomials associated with nowhere-zero flows, Journal of Combinatorial Theory Series B, vol. 84 (2002), pp. 260–269.
  28. M. Kochol: Equivalences between hamiltonicity and flow conjectures, and the sublinear defect property, Discrete Mathematics, vol. 254 (2002), pp. 221–230.
  29. M. Kochol: Tension polynomials of graphs, Journal of Graph Theory, vol. 40 (2002), pp. 137–146.
  30. H. Fleischner and M. Kochol: A note about the dominating circuit conjecture, Discrete Mathematics, vol. 259 (2002), pp. 307–309.
  31. M. Kochol, Linear algorithm for 3-coloring of locally connected graphs, in: Experimental and Efficient Algorithms, Editors: K. Jansen, M. Margraf, M. Mastrolli, J. D. P. Rolim, Lecture Notes in Computer Science, Vol. 2647, Springer-Verlag, Berlin, 2003, pp. 191–194.
  32. M. Kochol, V. Lozin and B. Randerath: The 3-colorability problem on graphs with maximum degree 4, SIAM Journal on Computing, vol. 32 (2003), pp. 1128–1139.
  33. M. Kochol: On bases of the cycle and cut spaces in digraphs, Ars Combinatoria, vol. 68 (2003), pp. 231-234.
  34. M. Kochol: About elementary cuts and flow polynomials, Graphs and Combinatorics, vol. 19 (2003), pp. 389-392.
  35. M. Kochol: Tension-flow polynomials on graphs, Discrete Mathematics, vol. 274 (2004), pp. 173-185
  36. M. Kochol: Reduction of the 5-flow conjecture to cyclically 6-edge-connected snarks, Journal of Combinatorial Theory Series B, vol. 90 (2004), 139-145.
  37. M. Kochol: Snarks and flow-snarks constructed from coloring-snarks, Discrete Mathematics, vol. 278 (2004), pp. 165-174.
  38. M. Kochol: Constructions of graphs without nowhere-zero flows from Boolean formulas, Ars Combinatoria, vol. 70 (2004), pp. 257-264.
  39. M. Kochol: A note on approximation of a ball by polytopes, Discrete Optimization, vol. 1 (2004), pp. 229-231.
  40. M.N. Ellingham, H. Fleischner, M. Kochol and E. Wenger: Colorability of planar graphs with isolated nontriangular faces, Graphs and Combinatorics, vol. 20 (2004), pp. 443-446.
  41. M. Kochol: Girth restriction for the 5-flow conjecture, Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 705-707.
  42. M. Kochol: 3-coloring and 3-clique-ordering of locally connected graphs, Journal of Algorithms, vol. 54 (2005), pp. 122-125.
  43. M. Kochol, N. Krivoňáková and S. Smejová: Approximation algorithms for chromatic index and edge-coloring of multigraphs, in: Experimantal and Efficient Algorithms, Editor: S.E. Nikoletseas, Lecture Notes in Computer Science, Vol. 3503, Springer-Verlag, Berlin, 2005, pp. 602-605.
  44. J. Balogh, M. Kochol, A Pluhár and X. Yu: Covering planar graphs with forests, Journal of Combinatorial Theory Series B, vol. 94 (2005), pp. 147–158.
  45. M. Kochol: Decomposition formula for the flow polynomial, European Journal of Combinatorics, vol. 26 (2005), pp. 1086-1093.
  46. M. Kochol, N. Krivoňáková and S. Smejová: Edge coloring of multigraphs, Discrete Mathematics, vol. 300 (2005), pp. 229-304.
  47. M. Kochol: About counterexamples to the 5-flow conjecture, Electronic Notes in Discrete Mathematics, vol. 22 (2005), pp. 21-24.
  48. M. Kochol: Restrictions on smallest counterexamples to the 5-flow conjecture, Combinatorica, vol. 26 (2006), pp. 83-89.
  49. M. Kochol, N. Krivoňáková, S. Smejová and K. Šranková, Nowhere-zero Z5-flows on wheels, Electronic Notes in Discrete Mathematics, vol. 28 (2007), pp. 103-107.
  50. M. Kochol, N. Krivoňáková, S. Smejová and K. Šranková, Approximation of 3-edge-coloring of cuic graphs, Electronic Notes in Discrete Mathematics, vol. 29 (2007), pp. 91-95.
  51. M. Kochol, N. Krivoňáková, S. Smejová and K. Šranková, Counting nowhere-zero flows on wheels, Discrete Mathematics, vol. 308 (2008), pp. 2050-2053.
  52. M. Kochol, N. Krivoňáková, S. Smejová and K. Šranková, Complexity of approximation of 3-edge-coloring of graphs, Information Processing Letters, vol. 108 (2008), pp. 238-241.
  53. M. Kochol, 3-Regular non 3-edge-colorable graphs with polyhedral embeddings in orientable surfaces,  in: Graph Drawing 2008, Editors: I.G. Tollis, M. Patrignani, Lecture Notes in Computer Science, Vol. 5417, Springer-Verlag, Berlin, 2009, pp. 319-323.
  54. M. Kochol, Polyhedral embeddings of snarks in orientable surfaces, Proceedings of the American Mathematical Society, vol. 137 (2009), pp. 1613-1619.
  55. M. Kochol, Smallest counterexample to the 5-flow conjecture has girth at least eleven, Journal of Combinatorial Theory, Series B, vol. 100 (2010), pp. 381-389.
  56. M. Kochol, Complexity of 3-edge-coloring in the class of cubic graphs with a polyhedral embedding in an orientable surface, Discrete Applied Mathematics, vol. 158 (2010), pp. 1856-1860.
  57. M. Kochol, N. Krivoňáková, S. Smejová and K. Šranková, Reductions of matrices associated with nowhere-zero flows, in: IWOCA 2010, Editors: C.S. Iliopoulos and W.F. Smyth, Lecture Notes in Computer Science, Vol. 6460, Springer-Verlag, Heidelberg, 2011, pp. 192-200.
  58. M. Kochol and R. Škrekovski, Dichotomy for coloring of dart graphs, in: IWOCA 2010, Editors: C.S. Iliopoulos and W.F. Smyth, Lecture Notes in Computer Science, Vol. 6460, Springer-Verlag, Heidelberg, 2011, pp. 82-89.
  59. M. Kochol, Three measures of edge-uncolorability, Discrete Mathematics, vol. 311 (2011), pp. 106-108.
  60. M. Kochol and N. Krivoňáková, Coefficients of chromatic polynomials and tension polynomials, Contributions to Discrete Mathematics, vol. 6 (2011), pp. 48-51.
  61. M. Kochol, N. Krivoňáková, S. Smejová and K. Šranková, Matrix reduction in a combinatorial computation, Information Processing Letters, vol. 111 (2011), pp. 164-168.
  62. M. Kochol and R. Škrekovski, Brooks’ theorem for generalized dart graphs, Information Processing Letters, vol. 112 (2012), pp. 200–204.
  63. M. Kochol, Non-extendible latin parallelepipeds, Information Processing Letters, vol. 112 (2012), pp. 942–943.
  64. M. Kochol, Linear algebraic approach to an edge-coloring result, Journal of Combinatorial Optimization, in press.