## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!

## #StackBounty: #cc.complexity-theory #graph-theory #sat #counting-complexity #planar-graphs Disproving \$oplus\$ETH by reducing \$oplus k…

### Bounty: 100

In this question and its answer, they discuss about reducing CNF-SAT with $$n$$ variables and $$m$$ clauses to a (problem on) planar graph $$G=(V,E)$$ with $$|V|$$ as small as possible. It is said that the best known reduction has $$|V| = m^2$$, and that if a better reduction with $$|V| in o(m^2)$$ is found, that would refute ETH.

There is a reduction from $$oplus k$$-SAT with $$n$$ variables and $$m$$ clauses to $$oplus$$VERTEX COVER where the output graph $$G=(V,E)$$ is planar and has $$|V| = 51(k+1)nm$$. Such reduction clearly meets the $$|V| in o(m^2)$$ requirement when $$k$$ is a constant and $$m$$ is superlinear in $$n$$.

Question
Can the same line of reasoning made within the linked question be applied here in order to refute $$oplus$$ETH, or am I missing some important detail?

Get this bounty!!!