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The Complexity of Counting Surjective Homomorphisms and Compactions
[article]

2019
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arXiv
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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 }. ...

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

2017
*
arXiv
*
pre-print

In this

arXiv:1710.01712v1
fatcat:u4p5ixsypfeercdzgvfiabvvbu
*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. ...##
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The Complexity of Counting Surjective Homomorphisms and Compactions
[chapter]

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 }. ...