Graph Algorithms and Applications I Volume 1

A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec­ trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of “starter” designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding “starter” designs.

The timeliness of a manuscript is more than its form, which may be unfinished or tentative. Thus, in some instances, proofs may be merely outlined and results presented which have been or will later be published elsewhere. If possible, a subject index should be included. Publication of Lecture Notes is intended as a service to the international mathematical community, in that a commercial publisher, Springer-Verlag, can offer a wide distribution of documents which would otherwise have a restricted readership. Once published and copyrighted, they can be documented in the scientific literature.

Alexandrov’s work was both original and extremely influential. This book gave rise to studying surfaces “in the large,” rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.

Since the beginning, the Hyperstructure Theory and particu- larly the Hypergroup Theory, had applications to several domains. Marty, who introduced hypergroups in 1934, applied them to groups, algebraic functions and rational fractions. New applications to groups were also found among others by Eaton, Ore, Krasner, Utumi, Drbohlav, Harrison, Roth, Mockor, Sureau and Haddad. Connections with other subjects of classical pure Mathematics have been determined and studied: * Fields by Krasner, Stratigopoulos and Massouros Ch. * Lattices by Mittas, Comer, Konstantinidou, Serafimidis, Leoreanu and Calugareanu * Rings by Nakano, Kemprasit, Yuwaree * Quasigroups and Groupoids by Koskas, Corsini, Kepka, Drbohlav, Nemec * Semigroups by Kepka, Drbohlav, Nemec, Yuwaree, Kempra- sit, Punkla, Leoreanu * Ordered Structures by Prenowitz, Corsini, Chvalina IX x * Combinatorics by Comer, Tallini, Migliorato, De Salvo, Scafati, Gionfriddo, Scorzoni * Vector Spaces by Mittas * Topology by Mittas , Konstantinidou * Ternary Algebras by Bandelt and Hedlikova.