List of Publications

 

 

Martin Kochol (2023)

 

 

  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, vol. 28 (2014), pp. 341–347.
  65. M. Kochol, Quantitative Methods for Nowhere-Zero Flows and Edge-Colorings, in: M. Dehmer, F. Emmert-Streib, Quantitative Graph Theory: Theoretical Foundations and Applications, pp. 141–180, Chapman and Hall/CRC Press, Boca Raton, FL, 2015.
  66. M. Kochol, Polynomial algorithms for canonical forms of orientations, Journal of Combinatorial Optimization, vol. 31 (2016) 218-222.
  67. M. Kochol, Edge cut splitting formulas for Tutte-Grothendieck invariants, Journal of Combinatorial Theory, Series B, vol. 125 (2017), pp. 114-131.
  68. M. Kochol, Three colorability characterized by shrinking of locally connected subgraphs into triangles, Information Processing Letters, vol. 135 (2018), pp. 33–35.
  69. M. Kochol, Equivalent versions of group-connectivity theorems and conjectures, Discrete Applied Mathematics, vol. 257 (2019), pp. 350–352.
  70. M. Kochol, Interpretations of the Tutte polynomials of regular matroids, Advances in Applied Mathematics, vol. 111 (2019), 101934.
  71. M. Kochol, Modifications of Tutte-Grothendieck invariants and Tutte polynomials, AKCE International Journal of Graphs and Combinatorics, vol. 17 (2020), pp. 70–73.
  72. M. Kochol, Bounds of characteristic polynomials of regular matroids, Contributions to Discrete Mathematics, vol. 15 (2020), pp. 98–107.
  73. M. Kochol, Interpretations of the Tutte and characteristic polynomials of matroids, Journal of Algebraic Combinatorics, vol. 53 (2021), pp. 1–9.
  74. M. Kochol, Polynomials counting nowhere-zero chains in graphs, The Electronic Journal of Combinatorics, vol. 29(1) (2022), #P1.19.
  75. M. Kochol, Interpretations for the Tutte polynomials of morphisms of matroids, Discrete Applied Mathematics 322 (2022), pp. 210–216.
  76. M. Kochol, One-to-one correspondence between interpretations of the Tutte polynomials, Journal of Combinatorial Theory, Series B 162 (2023), pp. 134–143
  77. M. Kochol, Linear algebraic relations among cardinalities of sets of matroid functions, Mathematics 11(11) (2023) 2570.