Name
Abstract | ||
|---|---|---|
We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite families of well-covered graphs, none of which have this property. We use these results to provide a minimal counterexample to a conjecture of Villarreal regarding Cohen–Macaulay graphs. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.disc.2018.07.029 | Discrete Mathematics |
Keywords | Field | DocType |
Well-covered graph,Vertex decomposable graph,Dominating set,Shedding vertices,Cohen–Macaulay graph | Discrete mathematics,Graph,Combinatorics,Dominating set,Vertex (geometry),Minimal counterexample,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
341 | 12 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan Baker | 1 | 0 | 0.34 |
| Kevin N. Vander Meulen | 2 | 17 | 5.27 |
| Adam Van Tuyl | 3 | 15 | 4.32 |