Peter Mih�k

2. 4. 1949 (Ko�ice, 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 Ko�ice
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. Semani�in), Discuss. Math. Graph Theory 31 (2011), no. 3, 559�575.
  2. Generalized circular colouring of graphs (with J. Oravcov�, R. Sot�k), 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; Ha�uszczak, Mariusz; Mih�k, 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. Mi�kuf, G. Semani�in), 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. Semani�in), 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. Semani�in), 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.