PREFACE

The origin of the study of graph decompositions and factorizations can be seen in various combinatorial problems, most of which, emerged in the 19th century. Among them the best known are Kirkman's problem of 15 strolling school girls, Dudney's problem of 9 handcuffed prisoners, Euler's problem of 36 army officers, Kirkman's problem of Knights, Lucas' dancing round problem and the four colour problem. Now-a-days, graph decomposition problems rank among the most prominent areas of research in Graph Theory and Combinatorics. Many combinatorial, algebraic and other mathematical structures are linked to decompositions of graphs which give their study a great theoretical importance. On the other hand results on graph decompositions can be applied in Coding Theory, Design of Experiments, X-ray Crystallography, Serology, Radio-astronomy, Radio-location, Computer and Communication Networks and other fields. In this thesis, we discuss several types of graph decomposition problems such as randomly packable graphs, common weight decompositions with respect to difference labelings and additive labelings, difference label-: ings and acyclic graphoidal covers, path double covers and decompositions of complete graphs into isomorphic C-cubes.