Residual reliability of P-threshold graphs

A.A. Chernyak
2004 Discrete Applied Mathematics  
We solve the problem of computing the residual reliability (the RES problem) for all classes of P-threshold graphs for which e cient structural characterizations based on decomposition to indecomposable components have been established. In particular, we give a constructive proof of existence of linear algorithms for computing residual reliability of pseudodomishold, domishold, matrogenic and matroidal graphs. On the other hand, we show that the RES problem is #P-complete on the class of
more » ... ar graphs, which implies the #P-completeness of the RES problem on the classes of indecomposable box-threshold and pseudothreshold graphs. ?
doi:10.1016/s0166-218x(02)00296-2 fatcat:chmal4g4mrdi3jhldeey37tioy