We give a new derivation of the threshold of appearance of the k-core of a random graph. Our method uses a hybrid model obtained from a simple model of random graphs based on rand...
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a random graph as the density of edges increases, and the transition of a rand...
We give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian generalized series-parallel graph, and show how to adapt this algorithm...