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Giorgio Camerani
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The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following equation holds (refer to the above article for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above article for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following equation holds (refer to the above article for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

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Giorgio Camerani
  • 6.9k
  • 1
  • 35
  • 64

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above referencearticle for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above reference for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above article for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

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Source Link
Giorgio Camerani
  • 6.9k
  • 1
  • 35
  • 64

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above reference for the proof):

$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above reference for the proof):

$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$

Counting vertex covers is #P-complete on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

The ODD EVEN DELTA problem is #P-hard, even on 3-regular bipartite planar graphs.

Let $\mathcal{C}$ be the set of vertex covers of a general graph $G$. Then, assuming $G$ has no isolated vertices, the following holds (refer to the above reference for the proof):

$$|\mathcal{C}| = 2^{|V|} - \sum_{k = 2}^{|V|} \Delta_k \cdot 2^{|V|-k}$$

Counting vertex covers is #P-complete even on 3-regular bipartite planar graphs, and it can be done with a linear number of calls to an ODD EVEN DELTA oracle.

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Giorgio Camerani
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Giorgio Camerani
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  • 35
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