Progress on perfect graphs
โ Scribed by Maria Chudnovsky; Neil Robertson; P. D. Seymour; Robin Thomas
- Book ID
- 106275344
- Publisher
- Springer-Verlag
- Year
- 2003
- Tongue
- English
- Weight
- 186 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0025-5610
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
An edge in a graph G is called a wing if it is one of the two nonincident edges of an induced P 4 (a path on four vertices) in G. For a graph G, its winggraph W (G) is defined as the graph whose vertices are the wings of G, and two vertices in W (G) are connected if the corresponding wings in G belo
A perfect graph is critical, if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We relate critically perfect graphs to well-known classes of perfect graphs, investigate the structure of the class of critically perfect graphs, a
Let i be a positive integer. We generalize the chromatic number x ( G ) of G and the clique number w(G) of G as follows: The i-chromatic number of G , denoted by x Z ( G ) , is the least number k for which G has a vertex partition V,, V,, . . . , Vk: such that the clique number of the subgraph induc