Name
Abstract | ||
|---|---|---|
A relational structure is (connected-)homogeneous if every isomorphism between finite (connected) substructures extends to an automorphism of the structure. We investigate notions which generalise (connected-)homogeneity, where "isomorphism" may be replaced by "homomorphism" or "monomorphism" in the definition. Specifically, we study the classes of finite connected-homomorphism-homogeneous graphs, with the aim of producing classifications. The main result is a classification of the finite C-HH graphs, where a graph G is C-HH if every homomorphism from a finite connected induced subgraph of G into G extends to an endomorphism of G. The finite C-II (connected-homogeneous) graphs were classified by Gardiner in 1976, and from this we obtain classifications of the finite C-HI and C-MI finite graphs. Although not all the classes of finite connected-homomorphism-homogeneous graphs are completely characterised, we may still obtain the final hierarchy picture for these classes. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1002/jgt.21788 | Journal of Graph Theory |
Keywords | Field | DocType |
homomorphisms | Topology,Discrete mathematics,Combinatorics,Indifference graph,Modular decomposition,Graph isomorphism,Chordal graph,Induced subgraph,Isomorphism,Homomorphism,Mathematics,Endomorphism | Journal |
Volume | Issue | Citations |
78 | 1 | 1 |
PageRank | References | Authors |
0.40 | 7 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Deborah C. Lockett | 1 | 1 | 0.40 |