| Abstract: | A graph is YΔY‐reducible if it can be reduced to a vertex by a sequence of series‐parallel reductions and YΔY‐transformations. Terminals are distinguished vertices, that cannot be deleted by reductions and transformations. In this article, we show that four‐terminal planar graphs are YΔY‐reducible when at least three of the vertices lie on the same face. Using this result, we characterize YΔY‐reducible projective‐planar graphs. We also consider terminals in projective‐planar graphs, and establish that graphs of crossing‐number one are YΔY‐reducible. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 83–93, 2000 |
