A digraph D is said to be an R-digraph (kernel-perfect graph) if all of its induced subdigraphs possesses a kernel (independent dominating subset). I show in this work that a digraph D, without directed triangles all of whose odd directed cycles C = (1, 2,..., 2n + 1, 1), possesses two short chords
Meyniel weakly triangulated graphs II: A theorem of Dirac
β Scribed by Ryan B. Hayward
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 477 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
β¦ Synopsis
WC gcneralizc a theorem due to Dirac and show that every Mcyniel weakly triangulated graph has some vertex which is not the middle vertex of any P;. Our main tool is a separating set notion known as a handle. 01997 Elsevicr Science B.V. k'c,~~ortl.s:
π SIMILAR VOLUMES
We prove that if G is a connected graph with p vertices and minimum degree greater than max( p/4 -1,3) then G2 is pancyclic. The result is best possible of its kind.
## Abstract The topological subgraph relation between cubic graphs is analyzed. The analysis is then applied to generalize a theorem of Dirac.
## Abstract One of the basic results in graph colouring is Brooks' theorem [R. L. Brooks, Proc Cambridge Phil Soc 37 (1941) 194β197], which asserts that the chromatic number of every connected graph, that is not a complete graph or an odd cycle, does not exceed its maximum degree. As an extension o