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A graph theoretical approach to the firebreak locating problem
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The Complexity of Morality: Checking Markov Blanket Consistency with DAGs via Morality
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Dichotomy for Graph Homomorphisms with Complex Values on Bounded Degree Graphs
The complexity of graph homomorphisms has been a subject of intense study [11, 12, 4, 42, 21, 17, 6, 20]. The partition function Z_π(Β·) of graph homomorphism is defined by a symmetric matrix π over β. We prove that the complexity dichotomy of [6] extends to bounded degree graphs. More precisely, we prove that either G β¦ Z_π(G) is computable in polynomialtime for every G, or for some Ξ > 0 it is #Phard over (simple) graphs G with maximum degree Ξ(G) β€Ξ. The tractability criterion on π for this dichotomy is explicit, and can be decided in polynomialtime in the size of π. We also show that the dichotomy is effective in that either a Ptime algorithm for, or a reduction from #SAT to, Z_π(Β·) can be constructed from π, in the respective cases.
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