Cuts and bounds
详细信息 查看全文
- 作者：Jaroslav Neš ; etř ; il and Patrice Ossona de Mendez
- 关键词：Homomorphism ; Homomorphism order ; Homomorphism extrema ; Cuts ; Bounds
- 刊名：Discrete Mathematics
- 出版年：2005
- 出版时间：28 October 2005
- 年：2005
- 卷：302
- 期：1-3
- 页码：211-224
- 全文大小：144 K
文摘
We consider the colouring (or homomorphism) order induced by all finite graphs and the existence of a homomorphism between them. This ordering may be seen as a lattice which is far from being complete. In this paper we study bounds and suprema and maximal elements in of some frequently studied classes of graphs (such as bounded degree, degenerated and classes determined by a finite set of forbidden subgraphs). We relate these extrema to cuts of subclasses of (cuts are finite sets which are comparable to every element of the class ). We determine all cuts for classes of degenerated graphs. For classes of bounded degree graphs this seems to be a very difficult problem which is also mirrored by the fact that these classes fail to have a supremum. We note a striking difference between undirected and oriented graphs. This is based on the recent work of C. Tardif and J. Nešetřil. Also minor closed classes are considered and we survey recent results obtained by authors. A bit surprisingly this order setting captures Hadwiger conjecture and suggests some new problems.