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:
 Unique factorization theorem for objectsystems (with G. Semanišin), Discuss. Math. Graph Theory 31 (2011), no. 3, 559–575.
 Generalized circular colouring of graphs (with J. Oravcová, R. Soták), Discuss. Math. Graph Theory 31 (2011), no. 2, 345–356.
 Generalized total colorings of graphs (with M. Borowiecki, A. Kemnitz, M. Marangio), Discuss. Math. Graph Theory 31 (2011), no. 2, 209–222.
 DrgasBurchardt, Ewa; Hałuszczak, Mariusz; Mihók, Peter Minimal forbidden graphs of reducible additive hereditary graph properties (with E. DrgasBurchardt, M. Haluszczak), Ars Combin. 95 (2010), 487–497.
 On universal graphs for homproperties (with J. Miškuf, G. Semanišin), Discuss. Math. Graph Theory 29 (2009), no. 2, 401–409.
 On infinite uniquely partitionable graphs and graph properties of finite character (with J. Bucko), Discuss. Math. Graph Theory 29 (2009), no. 2, 241–251.
 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.
 On invariants of hereditary graph properties (with G. Semanišin), Discrete Math. 307 (2007), no. 78, 958–963.
 [r,s,t]chromatic numbers and hereditary properties of graphs (with A. Kemnitz, M. Marangio), Discrete Math. 307 (2007), no. 78, 916–922.
 On uniquely partitionable relational structures and object systems (with J. Bucko), Discuss. Math. Graph Theory 26 (2006), no. 2, 281–289.
 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) 385390
 Erratum to: "Factorizations and characterizations of inducedhereditary and compositive properties" [J. Graph Theory 49 (2005), no. 1, 1127; 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) 261261
 On the lattice of additive hereditary properties of object systems. Tatra Mt. Math. Publ. 30 (2005) 155161
 Factorizations and characterizations of inducedhereditary and compositive properties. (with Farrugia A., Richter R.B., Semanisin G.) J. Graph Theory 49 (2005) 1127
 Cycle lengths and chromatic number of graphs. (with Schiermeyer I.) Discrete Math. 286 (2004) 147149
 Minimal vertex Ramsey graphs and minimal forbidden subgraphs. (with BorowieckaOlszewska M., DrgasBurchardt E.) Discrete Math. 286 (2004) 3136
 A note on the chromatic number of reducible hereditary properties graphs. (with Semanisin G.) Stud. Univ. Zilina Math. Ser. 16 (2003) 6166
 A note on the unique factorization theorem for properties of infinite graphs. (with Imrich W., Semanisin G.) Stud. Univ. Zilina Math. Ser. 16 (2003) 5154
 Prime ideals in the lattice of additive inducedhereditary graph properties. (with Berger A.J.) Discuss. Math. Graph Theory 23 (2003) 117127
 Factorization of complete 3uniform hypergraphs into isomorphic deltasystems. (with Hornak M.) Stud. Univ. Zilina Math. Ser. 15 (2002) 4148
 Criteria of the existence of uniquely partitionable graphs with respect to additive inducedhereditary properties. (with Broere I., Bucko J.) Discuss. Math. Graph Theory 22 (2002) 3137
 Graph coloring compactness theorems equivalent to BPI. (with Cowen R., Hechler S.) Sci. Math. Jpn. 56 (2002) 213223
 Meet and joinirreducibility of additive hereditary properties of graphs. (with Berger A.J., Broere I., Moagi S.J.T.) Discrete Math. 251 (2002) 1118
 Gallai's inequality for critical graphs of reducible hereditary properties. (with Skrekovski R.) Discuss. Math. Graph Theory 21 (2001) 167177
 Minimal reducible bounds for the class of kdegenerate graphs. Discrete Math. 236 (2001) 273279
 On graphs with a local hereditary property. (with Borowiecki M.) Discrete Math. 236 (2001) 5358
 Unique factorization theorem. Discuss. Math. Graph Theory 20 (2000) 143153
 Generalized colorings and inducedhereditary properties of graphs. Graph Theory Notes N.Y. 39 (2000) 1318
 Homproperties are uniquely factorizable into irreducible factors. (with Kratochvil J.) Discrete Math. 213 (2000) 189194
 Minimal reducible bounds for planar graphs. (with Borowiecki M., Broere I.) Discrete Math. 212 (2000) 1927
 Additive and hereditary properties of graphs are uniquely factorizable into irreducible factors. (with Semanisin G., Vasky R.) J. Graph Theory 33 (2000) 4453
 Generalized Ramsey theory and decomposable properties of graphs. (with Burr S.A., Jacobson M.S., Semanisin G.) Discuss. Math. Graph Theory 19 (1999) 199217
 Factorizations of properties of graphs. (with Broere I., Moagi S.J.T., Vasky R.) Discuss. Math. Graph Theory 19 (1999) 167174
 Remarks on the existence of uniquely partitionable planar graphs. (with Borowiecki M., Tuza Z., Voigt M.) Discuss. Math. Graph Theory 19 (1999) 159166
 Fractional Pcolourings and Pchoiceratio. (with Tuza Z., Voigt M.) Tatra Mt. Math. Publ. 18 (1999) 6977
 On uniquely partitionable planar graphs. (with Bucko J., Voigt M.) Discrete Math. 191 (1998) 149158
 A note on maximal kdegenerate graphs. (with Filakova Z., Semanisin G.) Math. Slovaca 47 (1997) 489498
 Graphs maximal with respect to homproperties. (with Kratochvil, J., Semanisin G.) Discuss. Math. Graph Theory 17 (1997) 7788
 On generalized list colourings of graphs. (with Borowiecki M., Broere I.) Discuss. Math. Graph Theory 17 (1997) 127132
 A survey of hereditary properties of graphs. (with Borowiecki M., Broere I., Frick M., Semanisin G.) Discuss. Math. Graph Theory 17 (1997) 550
 Partition problems and kernels of graphs. (with Broere I., Hajnal, P.) Discuss. Math. Graph Theory 17 (1997) 311313
 Uniquely partitionable graphs. (with Bucko J., Frick M., Vasky R.) Discuss. Math. Graph Theory 17 (1997) 103113
 The order of uniquely partitionable graphs. (with Broere I., Frick M.) Discuss. Math. Graph Theory 17 (1997) 115125
 On the minimal reducible bound for outerplanar and planar graphs. Discrete Math. 150 (1996) 431435
 Generalized list colourings of graphs. (with Borowiecki M., DrgasBurchardt E.) Discuss. Math. Graph Theory 15 (1995) 185193
 On the factorization of reducible properties of graphs into irreducible factors. (with Vasky R.) Discuss. Math. Graph Theory 15 (1995) 195203
 Sequences realizable by maximal kdegenerate graphs. (with Borowiecki M., Ivanco J., Semanisin G.) J. Graph Theory 19 (1995) 117124
 Reducible properties of graphs. (with Semanisin G.) Discuss. Math. Graph Theory 15 (1995) 1118
 An extension of Brooks'theorem. Annals of Discrete Math. 51 (1992), 235236
 Hereditary properties of graphs. (with Borowiecki M.) Advances in Graph Theory, ed. V.R. Kulli, Vishwa International Publications, 1991, 4269.
 On a class of Hamiltonian polytopes. (with Jendrol S.) Discrete Math. 71 (1988) 233241
 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, 5364.
 On graphs critical with respect to generalized independence
numbers. Coll. Math. Soc. J. Bolyai 52. Combinatorics, Eger,
1987, 417421.
 The Longestpath degree sequence. (with Borowiecki M.) Graph Theory Notes of New York, XIII:7, (1987), 1 p.
 Additive hereditary properties and uniquely partitionable graphs. Graphs, Hypergraphs and Matroids, Zielona Gora 1985, 4958.
 On (n,P)partitionable graphs. (with Borowiecki M.)
Graphs, Hypergraphs and Applications, Ed. H. Sachs,
TeubnerTexte, Leipzig 1985, 1518.
 On vertex partition numbers of graphs.
Graphs and Other Combinatorial Topics, Praha 1982,
TeubnerTexte, 183188.
 On graphs critical with respect to vertex partition numbers. Discrete Math. 37 (1981) 123126
 On the structure of the point arboricity critical graphs. Math. Slovaca 31 (1981) 101106
 On the pointarboricity critical graphs.
Graphs, Hypergraphs and Block Systems, Zielona Gora, 1976, 155161.