摘要：In the counting Graph Homomorphism problem (#GraphHom) the question is: Given graphs G,H, find the number of homomorphisms from G to H. This problem is generally #P-complete, moreover, Cygan et al. proved that unless the Exponential Time Hypothesis fails there is no algorithm that solves this problem in time O( V(H) ^o( V(G) )). This, however, does not rule out the possibility that faster algorithms exist for restricted problems of this kind. Wahlström proved that #GraphHom can be solved in plain exponential time, that is, in time O((2k+1)^( V(G) + V(H) ) poly( V(H) , V(G) )) provided H has clique width k. We generalize this result to a larger class of graphs, and also identify several other graph classes that admit a plain exponential algorithm for #GraphHom.
