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The Complexity of Counting Surjective Homomorphisms and Compactions [article]

Jacob Focke, Leslie Ann Goldberg, Stanislav Zivny
2019 arXiv   pre-print
Note that a star may have only one vertex since, for example, we could have |U | = 1 and |V | = 0.  ...  Note that the particular choice of edges {e 1 , . . . , e k } is not important when counting homomorphisms from an independent set of edges to H-N k (I t ) only depends on the numbers k and t.  ...  Clearly, H 10 has only one connected subgraph and we can choose S H 10 = {H 10 }.  ... 
arXiv:1706.08786v5 fatcat:enn5bdbcnjbtbmdkgjl7vhadfa

Note on "The Complexity of Counting Surjective Homomorphisms and Compactions" [article]

Holger Dell
2017 arXiv   pre-print
In this note, we give a short proof of a weaker result: Namely, we only prove the #P-hardness of the more general problem in which G may have loops.  ...  I thank Jacob Focke, Leslie Ann Goldberg, and Standa Živný for comments on an earlier version of this note, and for subsequent discussions at the Dagstuhl Seminar 17341 on "Computational Counting" in August  ...  For the case of VertSurj, note that deleting any vertices of H ∈ F again yields a graph in F.  ... 
arXiv:1710.01712v1 fatcat:u4p5ixsypfeercdzgvfiabvvbu

The Complexity of Counting Surjective Homomorphisms and Compactions [chapter]

Jacob Focke, Leslie Ann Goldberg, Stanislav Živný
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
Note that a star may have only one vertex since, for example, we could have |U | = 1 and |V | = 0. The size of a graph is the number of vertices that it has.  ...  Note that the particular choice of edges {e 1 , . . . , e k } is not important when counting homomorphisms from an independent set of edges to H-N k (I t ) only depends on the numbers k and t.  ...  Clearly, H 10 has only one connected subgraph and we can choose S H 10 = {H 10 }.  ... 
doi:10.1137/1.9781611975031.116 dblp:conf/soda/FockeGZ18 fatcat:rgvjpxbalnafppijqy6x6gomrq