Absolute retracts and varieties generated by chordal graphs
| Autor: | Cynthia Loten |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Class (set theory)
Structure (category theory) Mathematics::General Topology 0102 computer and information sciences Isometry (Riemannian geometry) 01 natural sciences Convexity Theoretical Computer Science Combinatorics Chordal graph Simple (abstract algebra) Chordal graphs Monophonic convexity Variety Discrete Mathematics and Combinatorics 0101 mathematics Hole Mathematics Discrete mathematics Epigraph 010102 general mathematics Hole base Absolute retract Retraction 010201 computation theory & mathematics Variety (universal algebra) |
| Zdroj: | Discrete Mathematics. 310(10-11):1507-1519 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2009.08.013 |
| Popis: | Graphs that are retracts of each supergraph in which they are isometric are called absolute retracts with respect to isometry, and their structure is well understood; for instance, in terms of building blocks (paths) and operations (products and retractions). We investigate the larger class of graphs that are retracts of each supergraph in which all of their holes are left unfilled. These are the absolute retracts with respect to holes, and we investigate their structure in terms of the same operations of products and retractions. We focus on a particular kind of hole (called a stretched hole), and describe a class of simple building blocks of the corresponding absolute retracts. Surprisingly, these also turn out to be precisely those absolute retracts that can be built from chordal graphs. Monophonic convexity is used to analyse holes on chordal graphs. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect