Homomorphisms and Structural Properties of Relational Systems

Preface My interest in graph homomorphisms dates back to the Spring School of Combinatorics in . e School is traditionally organised by the Department of Applied Mathematics of the Charles University in a hilly part of the Czech Republic; in  it was one of the few times when the Spring School was international not only in terms of its participants, but also in terms of its venue. Participants will never forget carrying a blackboard across the border between Germany and the Czech Republic and the exciting boat trip on the Vltava. e study text on homomorphisms [], specially prepared for the Spring School, aroused my curiosity that has eventually resulted in both my master's thesis and this doctoral dissertation. e study of graph homomorphisms was pioneered by G. Sabidussi, Z. Hedrlín and A. Pultr in the 's. It was part of an attempt to develop a theory of general mathematical structures in the framework of algebra and category theory. Many nice and important results have emerged from their work and the work of their followers. Even so, until recently many graph theorists would not include homomorphisms among the topics of central interest in graph theory. Nevertheless, graph homomorphisms and structural properties of graphs have recently attracted much attention of the mathematical community. e reason may be in part that the homomorphism point of view has proved useful in various areas ranging from colouring and graph reconstruction to applications in artificial intelligence, telecommunication, and even statistical physics. A book [] now exists that introduces the topic and brings together the most important parts of the theory and its applications. is thesis surveys my small contribution to the ongoing research in this area. I typeset the thesis using X E L A T E X. is new typesetting system based on Donald Knuth's T E X and the format L A T E X extends T E X's capabilities of handling Unicode input, multilingual and multi-script documents and especially modern OpenType fonts. When I first saw it, I liked the typeface of the font Andulka very much and have soon decided to use it for my thesis. For typesetting mathematics, I used AMS Euler [], an upright cursive font that tries to emulate a mathematician's style of handwriting mathematical formulas on a blackboard, which is upright rather than italic. Some results contained in this thesis have been published or accepted for …