We prove the conjecture made by \(\mathrm{O}\). V. Borodin in 1976 that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces a 2-degenerate graph. that is, a forest. c. 1995 Academic Press. Inc.
On decomposing a graph into nontrivial bonds
β Scribed by Sean McGuinness
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 206 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
We show that for every 2-connected bipartite graph which is not a multiple edge and which has no K 5 -minor there is an edge-disjoint collection of nontrivial bonds (i.e., not stars) which partition the edges of the graph.
π SIMILAR VOLUMES
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph.
Insertion of CO, into the transition metal-hydride bond of [RhmH,(PH,),]+, Cu'H(PH,),, and Rh'H(PH,), was theoretically investigated with ab initio MO/MP4, SD-CI, and CCD methods. The geometries of reactants, transition states (TS), and products were optimized at the Hartree-Fock level, and then M P