results have become classical, including results about graph relations, 1-factors and cubic graphs. As they were published only in Slovak, many of them remained unknown and some of the results were independently rediscovered much later by other mathematicians. In Canada he wrote more than 75 additional articles. His publications covers a wide range of topics in graph theory and combinatorics: convex polyhedra, quasigroups, special decompositions into Hamiltonian paths, Latin squares, decompositions of complete graphs, perfect systems of difference sets, additive sequences of permutations, tournaments and combinatorial games theory. One of his results, known as Kotzig's theorem, is the statement that every polyhedral graph has an edge whose two endpoints have total degree at most 13. An extreme case is the triakis icosahedron, where no edge has smaller total degree. Kotzig published the result in Slovakia in 1955, and it was named and popularized in the west by Branko Grünbaum in the mid-1970s. Kotzig published many open problems. One of them is the Ringel–Kotzig conjecture, stating that all trees have a graceful labeling. In 1963, Gerhard Ringel proposed that the complete graph could be decomposed into isomorphic copies of any given -vertex tree, and in 1966, Alexander Rosa credited Kotzig with the suggestion that a stronger decomposition always existed, equivalent to the existence of a graceful labeling. The question remains unsolved. Recognition In honor of Kotzig's 60th birthday, Alexander Rosa, Gert Sabidussi and Jean Turgeon edited a festschrift, Theory and Practice of Combinatorics: A collection of articles honoring Anton Kotzig on the occasion of his sixtieth birthday (Annals of Discrete Mathematics 12, North-Holland, 1982), with contributions from experts from around the world. In 1999, a commemorative plaque was erected on his birth house in Kočovce on the 80th anniversary of his birth. See also Kotzig transformations Ringel-Kotzig conjecture References External links Anton Kotzig, 1919–1991, Mathematica Slovaca 42:3 (1992) 381-383. Prof. Anton Kotzig's biography (in Slovak). Slovak mathematicians 20th-century Canadian mathematicians Graph theorists Université de Montréal faculty Charles University alumni Comenius University alumni Czechoslovak emigrants to Canada People from Nové Mesto nad Váhom District 1919 births 1991 deaths Czechoslovak mathematicians