Half-Graphs, Other Non-stable Degree Sequences, and the Switch Markov Chain

One of the simplest methods generating a random graph with given degree sequence is provided by Monte Carlo Markov Chain method using switches. The switch chain converges to uniform distribution, but generally rate convergence not known. After number results concerning various sequences, rapid mixing was established for so-called P-stable sequences (including that directed graphs), which covers every previously known rapidly region sequences.
 In this paper we give non-trivial family are and still on them. This has an intimate connection Tyshkevich-decompositions strong stability as well.