Bounds and Extrema for Classes of Graphs and Finite Structures

  • Jaroslav Nešetřil
Chapter
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 15)

Abstract

We consider the homomorphism (or colouring) order C induced by all finite structures (of a given type; for example graphs) and the existence of a homomorphism between them. This ordering may be seen as a lattice which is however far from being complete. In this paper we study (upper) bounds, suprema and maximal elements in C of some frequently studied classes of structures (such as classes of structures with bounded degree of its vertices, degenerated and classes determined by a finite set of forbidden substructures). We relate these extrema to cuts and duality theorems for C. Some of these results hold for general finite relational structures. In view of combinatorial problems related to coloring problems this should be regarded as a surprise. We support this view also by showing both analogies and striking differences between undirected and oriented graphs (i.e. for the easiest types) This is based on our recent work with C. Tardif.

Keywords

Connected Graph Undirected Graph Chromatic Number Homomorphic Image Great Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2006

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  1. 1.Department of Applied Mathematics and Institute of Thoretical Computer sciences (ITI)Charles UniversityPrahaCzech Republic

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