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
Special subdivisions ofK4and 4-chromatic graphs
✍ Scribed by Uffe Krusenstjerna-Hafstrøm; Bjarne Toft
- Publisher
- Springer Vienna
- Year
- 1980
- Tongue
- English
- Weight
- 526 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0026-9255
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let T2 be the graph obtained from the Petersen graph by first deleting a vertex and then contracting an edge incident to a vertex of degree two. We give a simple characterization of the graphs that contain no subdivision of T2. This characterization is used to show that if every planar r-graph is r-
We construct a family of 4-chromatic graphs which embed on the projective plane, and characterize the edge-critical members. The family includes many well known graphs, and also a new sequence of graphs, which serve to improve Gallai's bound on the length of the shortest odd circuit in a 4-chromatic
Let u,(G) denote the number of cycles of length k in a graph G. In this paper, we first prove that if G and H are X-equivalent graphs, then ak(G) = a,(H) for all k with g < k < $g -2, where g is the girth of G. This result will then be incorporated with a structural theorem obtained in [7] to show t