
Counting Maximum Matchings in Planar Graphs Is Hard
Here we prove that counting maximum matchings in planar, bipartite graph...
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Counting Polygon Triangulations is Hard
We prove that it is #Pcomplete to count the triangulations of a (nonsi...
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Counting perfect matchings and the eightvertex model
We study the approximation complexity of the partition function of the e...
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Filling the Complexity Gaps for Colouring Planar and Bounded Degree Graphs
We consider a natural restriction of the List Colouring problem: kRegul...
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The Complexity of Approximately Counting Retractions to SquareFree Graphs
A retraction is a homomorphism from a graph G to an induced subgraph H o...
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Enumeration of regular graphs by using the cluster in high efficiency
In this note, we proposed a method to enumerate regular graphs on the cl...
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Effectively Counting st Simple Paths in Directed Graphs
An important tool in analyzing complex social and information networks i...
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The Complexity of Counting Edge Colorings for Simple Graphs
We prove #Pcompleteness results for counting edge colorings on simple graphs. These strengthen the corresponding results on multigraphs from [4]. We prove that for any κ≥ r ≥ 3 counting κedge colorings on rregular simple graphs is #Pcomplete. Furthermore, we show that for planar rregular simple graphs where r ∈{3, 4, 5} counting edge colorings with ąp̨p̨ą colors for any κ≥ r is also #Pcomplete. As there are no planar rregular simple graphs for any r > 5, these statements cover all interesting cases in terms of the parameters (κ, r).
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