Korzhyk Volodymyr Pavlovych

Korzhik Vladimir Pavlovich

 

Education: Chernivtsi National University (specialty – physics, 1974).

 

Scientific degree: Doctor of sciences in physics and mathematics (01.01.08 – mathematical logic, algorithm theory and discrete mathematics, 2010).

 

Scientific title: Senior Research Fellow (since 1995).

 

Position: Leading Research Fellow.

 

Research interests: topological graph theory: studying embeddings and immersions of graphs in two-dimensional surfaces

 

Main scientific results:

 

1.     A simple proof of the Map Color Theorem for nonorientable surfaces.

2.     It is shown that there are constants  such that for every  the complete graph  has at least  nonisomorphic orientable and nonorientable minimal embeddings.

3.     A nontrivial lower bound on the maximal distance between two triangular embeddings of some complete graphs is found.

4.     Using Steiner triple systems,  nonorientable triangular embeddings of complete graphs with unboundedly large looseness are constructed.

5.     The 1-chromatic number of every surface, orientable or nonorientable, is found up to 10.

6.     It is shown that there are planar graphs having no proper 2-immersions in the plane.

7.     The 1-chromatic number of every nonorientable surface with large genus  is found up to 1.

Major publications:

1.     Korzhik V. A simple proof of the Map Color Theorem for nonorientable surfaces // Journal of Combinatorial Theory, Ser. B. – 2022. – Vol. 156. – P. 1 – 17.

2.     Korzhik V.   Planar graphs having no proper 2-immersions in the plane. I // Discrete Mathematics. – 2021.  –  V.  344. –  112482. – P. 1 – 26.

3.     Korzhik V.   Planar graphs having no proper 2-immersions in the plane. II // Discrete Mathematics. – 2021.  –  V.  344. –  112481. – P. 1 – 27.

4.     Korzhik V.   Planar graphs having no proper 2-immersions in the plane. III // Discrete Mathematics. – 2021.  –  V.  344. –  112516. – P. 1 – 15.

5.     Korzhik V.  A simple construction of exponentially many nonisomorphic orientable triangular embeddings of    // The Art of Discrete and Applied Mathematics. – 2021.  –  V.  4. – P. 1 – 7.

6.     Korzhik V.  Recursive constructions and nonisomorphic minimal nonorientable embeddings of complete graphs //  Discrete Mathematics – 2015. – V. 338. – P. 2186 – 2196.

7.     Korzhik V. Nonorientable biembeddings of cyclic Steiner triple systems generated by Scolem sequences // Discrete Mathematics – 2015. – V. 338. – P. 1345 – 1361.

8.     Korzhik V. Proper 1-immersions of graphs triangulating the plane // Discrete Mathematics. –  2013. –  V. 313. – P. 2673 – 2686.

9.     Korzhik V. Generating nonisomorphic quadrangular embeddings of a complete graph // Journal of Graph Theory. – 2013. – V.74. – P.133 –142.

10.  Korzhik V., Mohar B. Minimal obstructions for 1-immersions and hardness of 1-planarity testing // Journal of Graph Theory. 2013. – V. 72. – P. 30 – 70.

11.  Korzhik V. On the 1-chromatic number of nonorientable surfaces with large genus // Journal of Combinatorial Theory, Series B. – 2012. – V. 102. – P. 283 – 328.

12.  Korzhik V.  Exponentially many nonisomorphic genus embeddings of    // Discrete Mathematics. – 2010. – V. 310. – P. 2919 – 2924.

13.  Korzhik V.  Finite fields and the 1-chromatic number of orientable surfaces // Journal of Graph Theory. – 2010. – Vol. 63. – P. 179 – 184.

14.  Korzhik V.  Coloring vertices and faces of maps on surfaces // Discrete Mathematics. –  2010. –  V. 310. – P. 2504 – 2509.

15.  Korzhik V.  Complete triangulations of a given order generated from a multitude of nonisomorphic cubic graphs by current assignments // Journal of Graph Theory. – 2009. – V. 61. – P. 324 – 334.

16.  Grannell M., Korzhik V. Orientable biembeddings of cyclic Steiner triple  systems from   current assignments of the Mobius ladder graph // Discrete Mathematics. – 2009. – V. 309. –  P. 2847 – 2860.

17.  Korzhik V., Mohar B. Minimal obstructions for 1-immersions and hardness of 1-planarity testing // Graph Drawing 2008. – Lecture Notes in Computer Science. – V. 5417. – Berlin Heidelberg: Springer – Verlag. 2009. – P. 302 – 312.

18.  Korzhik V. Exponentially many nonisomorphic orientable triangular embeddings  of    // Discrete Mathematics. – 2009. – V. 309. – P. 852 –866.

19.  Korzhik V. Exponentially many nonisomorphic orientable triangular embeddings  of    //  Discrete Mathematics. – 2008. – V. 308. – P. 1046 – 1071.

20.  Korzhik V.,  Kwak Jin Ho. A new approach to constructing exponentially many nonisomorphic nonorientable triangular embeddings of complete graphs //  Discrete Mathematics. – 2008. – V. 308. – P. 1072 – 1079.

21.  Korzhik V. Minimal non-1-planar graphs //  Discrete Mathematics. – 2008. – V. 308. – P. 1319 – 1327.

22.  Korzhik V.,  Kwak Jin Ho. Nonorientable triangular embeddings of complete graphs with arbitrarily large looseness //  Discrete Mathematics. – 2008. – V. 308. – P. 3208 –  3212.

23.  Korzhik V. On the maximal distance between triangular embeddings of a complete graph // Journal of Combinatorial Theory, Ser. B. – 2006. – V. 96. – P. 426 – 435.

24.  Bennett G., Grannell M.,  Griggs T., Korzhik V.,  Siran J. Small surface trades in triangular embeddings // Discrete Mathematics. – 2006. – V. 306. – P. 2637 – 2646.

25.  Alekseyev V., Korzhik V. On the voltage-current transferring in topological graph theory // Ars Combinatoria. – 2005. – V. 74. – P. 331 – 349.

26.  Grannell M., Korzhik V. Nonorientable biembeddings of Steiner triple systems // Discrete Mathematics. – 2004. – V. 285. – P.121 – 126.

27.  Korzhik V., Voss H.-J.  Exponential families of nonisomorphic nonorientable genus embeddings of complete graphs // Journal of Combinatorial Theory, Ser. B. – 2004. – V. 91. – P. 253 – 287.

28.  Grannell M.,  Griggs T., Korzhik V.,  Siran J.  On the minimal nonzero distance between triangular embeddings of a complete graph // Discrete Mathematics. – 2003. – V. 269. – P. 149 – 160.

29.  Korzhik V., Voss H.-J.  Exponential families of  nonisomorphic nontriangular orientable genus embeddings of complete graphs //  Journal of Combinatorial Theory, Ser. B. – 2002. – V. 86. – P.186 – 211.

30.  Korzhik V. Another proof of the Map Color Theorem for nonorientable surfaces // Journal of Combinatorial Theory, Ser. B. – 2002. – V. 86. – P. 221 – 253.

31.  Korzhik V., Voss H.-J.  On the number of nonisomorphic orientable regular embeddings of complete graphs  // Journal of Combinatorial Theory, Ser. B. – 2001. – V. 81. – P. 58 – 76.

32.  Korzhik V. Triangular embeddings of    with unboundedly large   // Discrete Mathematics. – 1998. – Vol. 190. – P. 149 – 162.

33.  Korzhik V. Nonadditivity of the 1-genus of a graph // Discrete Mathematics. – 1998. – V. 184. – P. 253 – 258.

34.  Korzhik V. An infinite series of surfaces with known 1-chromatic number // Journal of Combinatorial Theory, Ser. B. – 1998. – V. 72. – P. 80 – 90.

35.  Korzhik V. A possibly infinite series of surfaces with known 1-chromatic number  // Discrete Mathematics. – 1997. – V. 173. – P. 137 – 149.

36.  Korzhik V. A tighter bounding interval for the 1-chromatic number of a surface  // Discrete Mathematics. – 1997. – V. 169. –  P. 95 – 120.                 

37.  Korzhik V. A nonorientable triangular embedding of    ,   // Discrete Mathematics. – 1995. – V. 141. – P. 195  – 211.

38.  Korzhik V. A lower bound for the one-chromatic number  of a surface // Journal of Combinatorial Theory, Ser. B. – 1994. – V. 61. – P. 40 – 56.                 

39.  Harary F., Korzhik V., Lavrencenko S. Realizing the chromatic number of triangulations of surfaces // Discrete Mathematics. – 1993. – V. 123. – P. 197–204.

40.  Àëåêñååâ Â. Á., Êîðæèê Â. Ï. Âëîæåíèÿ ãðàôîâ â ïîâåðõíîñòè è òåîðèÿ ãðàôîâ òîêîâ // Äèñêðåòíàÿ ìàòåìàòèêà. – 1990. – Ò. 2 – Ñ. 123 – 141. 

E-mail: korzhikvp@gmail.com