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π SIMILAR VOLUMES
## Abstract A graph is __Y__βΞβ__Y__ reducible if it can be reduced to a single vertex by a sequence of seriesβparallel reductions and __Y__βΞβ__Y__ transformations. The class of __Y__βΞβ__Y__ reducible graphs is minor closed. We found a large number of minor minimal __Y__βΞβ__Y__ irreducible graph
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-
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 f
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