Jorma Kyppö, whose master's thesis deals with the Four Colour Problem and licentiate thesis with topological graph theory (embedding of non-planar graphs on the complex surfaces), did earlier focus on graph colouring algorithms and combinatorics of graph embeddings. Today he explores the structure of graphs embedded in complex chesslike games. He also has some interest with social networks and cognitive sociosemantic graphs. which are more intricate than general planar graphs.
TOPOLOGICAL GRAPH THEORY AND ALGORITHMS OF GRAPH COLOURING
"Karttojen neliväritysongelma, tausta ja perusteet" ("The Four Colour Conjecture"), sovelletun matematiikan pro gradu työ, Jyväskylän yliopisto, 1989. (Finnish)
"Embedding of Non-Triangular Graphs in the k-Toroids", paper presented in the Fourth Czechoslovak Symposium on Combinatorics, Prachatice, 1990, Computer Science Reports, WP-17, ISBN 951-680-369-5
"Embedding of Complete Graphs: Maximum Genus and the Extension of Heawood's Number", in Kilp M., Nummert U. (Eds.), Proceedings of the First Estonian Conference on Graphs and Applications, Dedicated to the 70th Birthday of Professor Frank Harary , Tartu University, 1991, pp. 148-161
"Graphs and Knots", Workshop on Graphs and Knots, Jyväskylä, Finland, June 1992."Avaruusverkkojen kuvaaminen", ("Representing of Nonplanar Graphs") tietojenkäsittelyopin pro gradu -työ, Jyväskylän yliopisto, 1993. (Finnish)
"Notes On Non-cellular Graph Embeddings", presented in The Workshop Graph Embeddings and Maps on Surfaces, Donovaly, Slovakia, August , 21 - 26, 1994.
"Colouring the Boundaries of Maps", presented in the 3nd International Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 1994.
"Verkkojen ja karttojen upottaminen eikonvekseille topologisille pinnoille" ("Embedding of Graphs and Maps in the Non Convex Surfaces"), Department of Computer Science and Information Systems, University of Jyväskylä, 1994. (Licentiate thesis, Finnish)
"Multinomial Formula and Arithmetical Tetrahedron", The 15th British Combinatorial Conference, Stirling, Scotland, 1995.
APPLICATIONS OF STRATEGY GAMES IN GRAPH THEORY
A research by-product, the chess for three players TriChess (*), has been developed for analyzing some models in the graph theory. TriChess is a strategy game making use of the mathematics and history of traditional chess. It exploits a universal idea of strategy games. Due to the number of players, completely different strategic combinations are used and it is often compared to the games of great powers in the political or commercial life. The computer version of Universal Chess may run several complicated chess modifications. As a result of this research, several connections to the commercial world have been created. Some interdisciplinary research studies have been made in the fields of programming, multimedia, game theory, economics and electronic commerce. Research is supported by the Jyväskylä Science Park.
(*) The name "TriChess" was given by professor Frank Harary in May 1993.
"The Knight's Tour and Path on Nonrectangular Chessboards", presented in the 2nd International Workshop on Cycles and Colourings, Novy Smokovec, Slovakia, September 1993
"Artificial Knights on Artificial Chessboards", The 9th Cumberland Conference University of Mississippi, Louisiana, USA, May 1996.
Patent: "Peli, erityisesti shakkipeli" ("Game, Especially Chess"), Hyödyllisyysmalli No 2844, Patentti ja rekisterihallitus, 1997.
"Kolmishakki universaalin shakin ilmentymänä" ("Trichess and Universal Chess"), Pelit, tietokone ja ihminen -seminaari, Suomen Tekoälyseura ja Taideteollinen korkeakoulu, Suomen Tekoälyseuran (Finnish Artificial Intelligence Society, FAIS) julkaisuja - Symposiosarja - No 15, Suomen tekoälyseura, VTT Tietotekniikka, Helsinki, 1999, ss. 113-123. (Finnish)
"Knight's Paths: New Problem Fields", presented in the 8th Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 1999.
Patent: "Pelilauta kolmea pelaajaa varten" ("The Gameboard for three players"), Hyödyllisyysmalli No 3797, Patentti ja rekisterihallitus, 1999.
"Artificial knights on artificial n-dimensional chessboards", presented in the 10th Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 2001.
"Three-Person Chess", lectures presented in the Illinois Institute of Technology on 2nd November 2001, Celebration in Honor of Frank Harary's 80th Birthday and in the University of New Mexico on 7th November 2001.
"Graphs Embeddings in Universal Chess", presented in the 12th Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 2003.
"Monen pelaajan symmetriset asetelmat shakin pohjalta" ("Symmetric N-person games and Chess"), Digitaalisten pelien maailmoja, Game Lab, Agora Center ja Koulutuksen tutkimuslaitos, Jyväskylän yliopisto, Jyväskylä, 2004, ss. 319-334. (Finnish)
"Graph structures in Universal Chess, some paths in Four Dimensional Chess" ("Graafistruktuurid universaalses males, mõned teed neljadimensioonilises males"), presented in The Second Estonian Conference on Graphs and Applications, Tallinn, Estonia, EuroUniversity, September 2006. Baltic Horizons, EuroUniversity Series, Special issue dedicated to 270 years of Graph Theory, pp. 23-32
"Paths in Universal Chess; hyper-knight's moves", presented in the 17th Workshop on Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 2008.
"The Cycles of Extended Knights", presented in the 19th Workshop on Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 2010.
"The Enumeration of Knight Graphs", presented in The 23th British Combinatorial Conference, Exeter, England, July 2011.
"Odd and Even Cycles in Digraphs of Small Strategy Games", presented in the 20th Workshop on Workshop on Cycles and Colourings, Novy Smokovec, Slovakia, September 2011.
OTHER GRAPH THEORY
"Designing People's’ Interconnections in Mobile Social Networks", with Giuseppe Lugano and Pertti Saariluoma, presented in International Conference on Multidisciplinary Information Sciences & Technologies (InScit2006), Merida (Spain), 25-27.10.2006."Constructing sociosemantic graphs", presented in the Conference on Semigroups, Acts and Categories with Applications to Graphs, University of Tartu, Estonia, June 2007. "Cycles and Colourings of Sociosemantic Graphs", presented in the 16th Workshop on Workshop on Cycles and Colourings, Stara Lesna, Slovakia, September 2007.
"Tracing potential school shooters in the digital sphere", with Jari Veijalainen and Alexander Semenov, Communications in Computer and Information Science, Volume 76, 163-178, 2010.
"Analyzing the presence of school shooting related communities at social media sites", with Jari Veijalainen and Alexander Semenov, International Journal of Multimedia Intelligence and Security Volume 1, Number 3 / 2010.
"The Number of A Graph", presented in The 24th Cumberland Conference, University of Louisiana, Kentucky, USA, May 2011.
"Induced Cycles of the Pascal's Polytopes", presented in the 21th Workshop on Workshop on Cycles and Colourings, Novy Smokovec, Slovakia, September 2012.
"Java-ohjelmointi Pro training", with Mika Vesterholm, (a study book in Finnish), Satku-Kauppakaari, Talentum Media Ltd, Helsinki, 2001, 400 pages. "Java-ohjelmointi, Valikkosarja", with Mika Vesterholm, (a study book in Finnish), Talentum Media Ltd, Helsinki, 2. ed. 2002, 400 pages, 3.& 4. ed. 2003, 514 pages, 5. ed. 2004, 512 pages, 6. ed. 2006, 566 pages, 7. & 8. ed. 2008 & 2010, 606 pages.