In the 1960's, Tutte presented a decomposition of a 2-connected finite graph into 3-connected graphs, cycles and bonds. This decomposition has been used to reduce problems on...
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more ge...
We present an expected polynomial time algorithm to generate a 2-connected unlabeled planar graph uniformly at random. To do this we first derive recurrence formulas to count the ...