Peter Mihók

2. 4. 1949 (Košice, Slovakia) – 27. 3. 2012 (Michigan, USA)


University Studies:
University of P. J. Safarik in Kosice, School of Natural Sciences (1967 – 1972),
RNDr. 1976, CSc. (PhD, advisor Prof. RNDr. Ernest Jucovic, DrSc.) 1983, Docent 1987

Positions held:
1972 – 1996 University of P. J. Safarik in Kosice, Faculty of Natural Sciences (Associate Prof.)
1996 – 2012 Math. Inst. Slovak Acad. Sci., Extension in Košice
1999 – 2011 Faculty of Economics, Technical University in Kosice

Field of Interest: Graph Theory

List of Publications:

  1. Unique factorization theorem for object-systems (with G. Semanišin), Discuss. Math. Graph Theory 31 (2011), no. 3, 559–575.
  2. Generalized circular colouring of graphs (with J. Oravcová, R. Soták), Discuss. Math. Graph Theory 31 (2011), no. 2, 345–356.
  3. Generalized total colorings of graphs (with M. Borowiecki, A. Kemnitz, M. Marangio), Discuss. Math. Graph Theory 31 (2011), no. 2, 209–222.
  4. Drgas-Burchardt, Ewa; Hałuszczak, Mariusz; Mihók, Peter Minimal forbidden graphs of reducible additive hereditary graph properties (with E. Drgas-Burchardt, M. Haluszczak), Ars Combin. 95 (2010), 487–497.
  5. On universal graphs for hom-properties (with J. Miškuf, G. Semanišin), Discuss. Math. Graph Theory 29 (2009), no. 2, 401–409.
  6. On infinite uniquely partitionable graphs and graph properties of finite character (with J. Bucko), Discuss. Math. Graph Theory 29 (2009), no. 2, 241–251.
  7. Unique factorization theorem and formal concept analysis (with G. Semanišin), In: Concept lattices and their applications, 232–239, Lecture Notes in Comput. Sci., 4923, Springer, Berlin, 2008.
  8. On invariants of hereditary graph properties (with G. Semanišin), Discrete Math. 307 (2007), no. 7-8, 958–963.
  9. [r,s,t]-chromatic numbers and hereditary properties of graphs (with A. Kemnitz, M. Marangio), Discrete Math. 307 (2007), no. 7-8, 916–922.
  10. On uniquely partitionable relational structures and object systems (with J. Bucko), Discuss. Math. Graph Theory 26 (2006), no. 2, 281–289.
  11. A note on maximal common subgraphs of the Dirac's family of graphs. (with Bucko J., Sacle J.-F., Wozniak M.), Discuss. Math. Graph Theory 25 (2005) 385-390
  12. Erratum to: "Factorizations and characterizations of induced-hereditary and compositive properties" [J. Graph Theory 49 (2005), no. 1, 11--27; MR2130467 ] by A. Farrugia, P. Mihok, R.B. Richter and G. Semanisin. (with Farrugia A., Richter R.B., Semanisin G.) J. Graph Theory 50 (2005) 261-261
  13. On the lattice of additive hereditary properties of object systems. Tatra Mt. Math. Publ. 30 (2005) 155-161
  14. Factorizations and characterizations of induced-hereditary and compositive properties. (with Farrugia A., Richter R.B., Semanisin G.) J. Graph Theory 49 (2005) 11-27
  15. Cycle lengths and chromatic number of graphs. (with Schiermeyer I.) Discrete Math. 286 (2004) 147-149
  16. Minimal vertex Ramsey graphs and minimal forbidden subgraphs. (with Borowiecka-Olszewska M., Drgas-Burchardt E.) Discrete Math. 286 (2004) 31-36
  17. A note on the chromatic number of reducible hereditary properties graphs. (with Semanisin G.) Stud. Univ. Zilina Math. Ser. 16 (2003) 61-66
  18. A note on the unique factorization theorem for properties of infinite graphs. (with Imrich W., Semanisin G.) Stud. Univ. Zilina Math. Ser. 16 (2003) 51-54
  19. Prime ideals in the lattice of additive induced-hereditary graph properties. (with Berger A.J.) Discuss. Math. Graph Theory 23 (2003) 117-127
  20. Factorization of complete 3-uniform hypergraphs into isomorphic delta-systems. (with Hornak M.) Stud. Univ. Zilina Math. Ser. 15 (2002) 41-48
  21. Criteria of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties. (with Broere I., Bucko J.) Discuss. Math. Graph Theory 22 (2002) 31-37
  22. Graph coloring compactness theorems equivalent to BPI. (with Cowen R., Hechler S.) Sci. Math. Jpn. 56 (2002) 213-223
  23. Meet- and join-irreducibility of additive hereditary properties of graphs. (with Berger A.J., Broere I., Moagi S.J.T.) Discrete Math. 251 (2002) 11-18
  24. Gallai's inequality for critical graphs of reducible hereditary properties. (with Skrekovski R.) Discuss. Math. Graph Theory 21 (2001) 167-177
  25. Minimal reducible bounds for the class of k-degenerate graphs. Discrete Math. 236 (2001) 273-279
  26. On graphs with a local hereditary property. (with Borowiecki M.) Discrete Math. 236 (2001) 53-58
  27. Unique factorization theorem. Discuss. Math. Graph Theory 20 (2000) 143-153
  28. Generalized colorings and induced-hereditary properties of graphs. Graph Theory Notes N.Y. 39 (2000) 13-18
  29. Hom-properties are uniquely factorizable into irreducible factors. (with Kratochvil J.) Discrete Math. 213 (2000) 189-194
  30. Minimal reducible bounds for planar graphs. (with Borowiecki M., Broere I.) Discrete Math. 212 (2000) 19-27
  31. Additive and hereditary properties of graphs are uniquely factorizable into irreducible factors. (with Semanisin G., Vasky R.) J. Graph Theory 33 (2000) 44-53
  32. Generalized Ramsey theory and decomposable properties of graphs. (with Burr S.A., Jacobson M.S., Semanisin G.) Discuss. Math. Graph Theory 19 (1999) 199-217
  33. Factorizations of properties of graphs. (with Broere I., Moagi S.J.T., Vasky R.) Discuss. Math. Graph Theory 19 (1999) 167-174
  34. Remarks on the existence of uniquely partitionable planar graphs. (with Borowiecki M., Tuza Z., Voigt M.) Discuss. Math. Graph Theory 19 (1999) 159-166
  35. Fractional P-colourings and P-choice-ratio. (with Tuza Z., Voigt M.) Tatra Mt. Math. Publ. 18 (1999) 69-77
  36. On uniquely partitionable planar graphs. (with Bucko J., Voigt M.) Discrete Math. 191 (1998) 149-158
  37. A note on maximal k-degenerate graphs. (with Filakova Z., Semanisin G.) Math. Slovaca 47 (1997) 489-498
  38. Graphs maximal with respect to hom-properties. (with Kratochvil, J., Semanisin G.) Discuss. Math. Graph Theory 17 (1997) 77-88
  39. On generalized list colourings of graphs. (with Borowiecki M., Broere I.) Discuss. Math. Graph Theory 17 (1997) 127-132
  40. A survey of hereditary properties of graphs. (with Borowiecki M., Broere I., Frick M., Semanisin G.) Discuss. Math. Graph Theory 17 (1997) 5-50
  41. Partition problems and kernels of graphs. (with Broere I., Hajnal, P.) Discuss. Math. Graph Theory 17 (1997) 311-313
  42. Uniquely partitionable graphs. (with Bucko J., Frick M., Vasky R.) Discuss. Math. Graph Theory 17 (1997) 103-113
  43. The order of uniquely partitionable graphs. (with Broere I., Frick M.) Discuss. Math. Graph Theory 17 (1997) 115-125
  44. On the minimal reducible bound for outerplanar and planar graphs. Discrete Math. 150 (1996) 431-435
  45. Generalized list colourings of graphs. (with Borowiecki M., Drgas-Burchardt E.) Discuss. Math. Graph Theory 15 (1995) 185-193
  46. On the factorization of reducible properties of graphs into irreducible factors. (with Vasky R.) Discuss. Math. Graph Theory 15 (1995) 195-203
  47. Sequences realizable by maximal k-degenerate graphs. (with Borowiecki M., Ivanco J., Semanisin G.) J. Graph Theory 19 (1995) 117-124
  48. Reducible properties of graphs. (with Semanisin G.) Discuss. Math. Graph Theory 15 (1995) 11-18
  49. An extension of Brooks'theorem. Annals of Discrete Math. 51 (1992), 235-236
  50. Hereditary properties of graphs. (with Borowiecki M.) Advances in Graph Theory, ed. V.R. Kulli, Vishwa International Publications, 1991, 42--69.
  51. On a class of Hamiltonian polytopes. (with Jendrol S.) Discrete Math. 71 (1988) 233-241
  52. On graphs matroidal with respect to additive hereditary properties. Graphs, Hypergraphs and Matroids II. Proc. of the Sixth Sc. Session of Math., Zielona Gora 1987, 53--64.
  53. On graphs critical with respect to generalized independence numbers. Coll. Math. Soc. J. Bolyai 52. Combinatorics, Eger, 1987, 417--421.
  54. The Longest-path degree sequence. (with Borowiecki M.) Graph Theory Notes of New York, XIII:7, (1987), 1 p.
  55. Additive hereditary properties and uniquely partitionable graphs. Graphs, Hypergraphs and Matroids, Zielona Gora 1985, 49--58.
  56. On (n,P)-partitionable graphs. (with Borowiecki M.) Graphs, Hypergraphs and Applications, Ed. H. Sachs, Teubner-Texte, Leipzig 1985, 15--18.
  57. On vertex partition numbers of graphs. Graphs and Other Combinatorial Topics, Praha 1982, Teubner-Texte, 183--188.
  58. On graphs critical with respect to vertex partition numbers. Discrete Math. 37 (1981) 123-126
  59. On the structure of the point arboricity critical graphs. Math. Slovaca 31 (1981) 101-106
  60. On the point-arboricity critical graphs. Graphs, Hypergraphs and Block Systems, Zielona Gora, 1976, 155-161.