A graph is Y ∆Y -reducible if it can be reduced to a vertex by a sequence of series-parallel reductions and Y ∆Y -transformations. Terminals are dis-
On terminal delta-wye reducibility of planar graphs
✍ Scribed by Isidoro Gitler; Feliú Sagols
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 614 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
✦ Synopsis
We prove terminal -Y reducibility of planar graphs with at most three terminals. The most important consequence of our proof is that this implicitly gives an efficient algorithm with time complexity O(|E (G)| 4 ) for reducibility of planar graphs G with at most three terminals. It also can be used for restricted reducibility problems with more terminals. Our proof uses a very well-known translation from these operations to transformations on the medial graph.
📜 SIMILAR VOLUMES
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
Let L be the set of all additive and hereditary properties of graphs. For P1, P2 E L we define the reducible property R = P1P2 as follows: G E PtP2 if there is a bipartition (V~,/1"2) of V(G) such that (V~) E Pi and (V2) E P2. For a property P E L, a reducible property R is called a minimal reducibl