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- W2067653823 abstract "We prove a complexity dichotomy theorem for a class of partition functions over k-regular graphs, for any fixed k. These problems can be viewed as graph homomorphisms from an arbitrary k-regular input graph G to the weighted two vertex graph on {0,1} defined by a real-valued symmetric function h. We completely classify the computational complexity of this problem. We show that there are exactly the following alternatives, for any given h. Depending on h, over k-regular graphs, either the problem is #P-hard even for planar graphs, the problem is #P-hard for general (non-planar) graphs, but solvable in polynomial time for planar graphs, or the problem is solvable in polynomial time for general graphs." @default.
- W2067653823 created "2016-06-24" @default.
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- W2067653823 date "2013-07-01" @default.
- W2067653823 modified "2023-10-16" @default.
- W2067653823 title "Partition functions on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>k</mml:mi></mml:math>-regular graphs with<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif display=inline overflow=scroll><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:math>-vertex assignments and real edge functions" @default.
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- W2067653823 doi "https://doi.org/10.1016/j.tcs.2012.12.043" @default.
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