A graph is Y βY -reducible if it can be reduced to a vertex by a sequence of series-parallel reductions and Y βY -transformations. Terminals are dis-
On the delta-wye reduction for planar graphs
β Scribed by K. Truemper
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 367 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
We provide an elementary proof of an important theorem by G. V. Epifanov, according to which every two-terminal planar graph satisfying certain connectivity restrictions can by some sequence of series/parallel reductions and delta-wye exchanges be reduced to the graph consisting of the two terminals and just one edge.
π SIMILAR VOLUMES
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree β. The conjecture has been proved to be true for graphs having β =
In a recent paper, Carsten Thomassen [Carsten Thomassen, Planarity and duality of finite and infinite graphs. J. Combinatorial Theory Ser. B 29 (1980) 244-2711 has shown that a number of criteria for the planarity of a graph can be reduced to that of Kuratowski. Here we present another criterion whi
## Abstract It is known that a planar graph on __n__ vertices has branchβwidth/treeβwidth bounded by $\alpha \sqrt {n}$. In many algorithmic applications, it is useful to have a small bound on the constant Ξ±. We give a proof of the best, so far, upper bound for the constant Ξ±. In particular, for th
## Abstract We prove in this note that the linear vertexβarboricity of any planar graph is at most three, which confirms a conjecture due to Broere and Mynhardt, and others.