On Generalizations of Matching-covered Graphs
✍ Scribed by Zoltán Szigeti
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 184 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
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📜 SIMILAR VOLUMES
We give a very simple proof that every non-bipartite matching covered graph contains a nice subgraph that is an odd subdivision of K 4 or C 6 . It follows immediately that every brick different from K 4 and C 6 has an edge whose removal preserves the matching covered property. These are classical an
A Petersen brick is a graph whose underlying simple graph is isomorphic to the Petersen graph. For a matching covered graph G, b(G) denotes the number of bricks of G, and p(G) denotes the number of Petersen bricks of G. An ear decomposition of G is optimal if, among all ear decompositions of G, it u
## Abstract In graph theory, the related problems of deciding when a set of vertices or a set of edges constitutes a maximum matching or a minimum covering have been extensively studied. In this paper we generalize these ideas by defining total matchings and total coverings, and show that these set
A set of points in a graph is independent if no two points in the set are adjacent. A graph is well covered if every maximal independent set is a maximum independent set or, equivalently, if every independent set is contained in a maximum independent set. The well-covered graphs are classified by th
## Abstract In this paper, we focus our attention on join‐covered graphs, that is, ±1‐weighted graphs, without negative circuits, in which every edge lies in a zero‐weight circuit. Join covered graphs are a natural generalization of matching‐covered graphs. Many important properties of matching cov