Mixing
A graph-coloring problem where only some of the edges should be bichromatic
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In a standard graph-coloring problem, it is required that all edges will be bichromatic (i.e., all edges should be connected to two vertices with different colors). What is a term, and some basic references, for a graph-coloring problem in which only a fraction of the edges should satisfy this condition? For example, at least $frac23$ or at least $frac12$?
I looked for "fractional coloring" but, apparently, it is a completely different problem.
graph-theory reference-request terminology coloring
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
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show 1 more comment
6
$begingroup$
In a standard graph-coloring problem, it is required that all edges will be bichromatic (i.e., all edges should be connected to two vertices with different colors). What is a term, and some basic references, for a graph-coloring problem in which only a fraction of the edges should satisfy this condition? For example, at least $frac23$ or at least $frac12$?
I looked for "fractional coloring" but, apparently, it is a completely different problem.
graph-theory reference-request terminology coloring
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
$endgroup$
$begingroup$
"Partial proper colouring", maybe?
$endgroup$
– EdOverflow
Jan 6 at 20:49
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what does bichromatic mean?
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– nafhgood
Jan 7 at 1:05
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@mathnoob I added an explanation
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– Erel Segal-Halevi
Jan 7 at 3:53
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@EdOverflow I found this expression here: arxiv.org/pdf/1810.06704.pdf If I understand correctly, it refers to coloring in which only some of the vertices are colored, while others are not colored at all.
$endgroup$
– Erel Segal-Halevi
Jan 7 at 4:18
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@erel-segal-halevi, yes, although the bichromatic property still holds for those that are coloured. I think the only downside to the term I suggested is that it implies the remaining vertices are not coloured at all (or not necessarily coloured). Maybe you could combine the termsproper colouringandsubgraphsto describe what you are after above. I would need to look into this a bit more before I can suggest a more concrete term.
$endgroup$
– EdOverflow
Jan 7 at 19:08
|
show 1 more comment
6
6
6
$begingroup$
In a standard graph-coloring problem, it is required that all edges will be bichromatic (i.e., all edges should be connected to two vertices with different colors). What is a term, and some basic references, for a graph-coloring problem in which only a fraction of the edges should satisfy this condition? For example, at least $frac23$ or at least $frac12$?
I looked for "fractional coloring" but, apparently, it is a completely different problem.
graph-theory reference-request terminology coloring
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
$endgroup$
In a standard graph-coloring problem, it is required that all edges will be bichromatic (i.e., all edges should be connected to two vertices with different colors). What is a term, and some basic references, for a graph-coloring problem in which only a fraction of the edges should satisfy this condition? For example, at least $frac23$ or at least $frac12$?
I looked for "fractional coloring" but, apparently, it is a completely different problem.
graph-theory reference-request terminology coloring
graph-theory reference-request terminology coloring
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
edited Jan 7 at 3:52
Erel Segal-Halevi
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
asked Jan 6 at 19:51
Erel Segal-HaleviErel Segal-Halevi
4,24611760
4,24611760
$begingroup$
"Partial proper colouring", maybe?
$endgroup$
– EdOverflow
Jan 6 at 20:49
$begingroup$
what does bichromatic mean?
$endgroup$
– nafhgood
Jan 7 at 1:05
$begingroup$
@mathnoob I added an explanation
$endgroup$
– Erel Segal-Halevi
Jan 7 at 3:53
$begingroup$
@EdOverflow I found this expression here: arxiv.org/pdf/1810.06704.pdf If I understand correctly, it refers to coloring in which only some of the vertices are colored, while others are not colored at all.
$endgroup$
– Erel Segal-Halevi
Jan 7 at 4:18
$begingroup$
@erel-segal-halevi, yes, although the bichromatic property still holds for those that are coloured. I think the only downside to the term I suggested is that it implies the remaining vertices are not coloured at all (or not necessarily coloured). Maybe you could combine the termsproper colouringandsubgraphsto describe what you are after above. I would need to look into this a bit more before I can suggest a more concrete term.
$endgroup$
– EdOverflow
Jan 7 at 19:08
|
show 1 more comment
$begingroup$
"Partial proper colouring", maybe?
$endgroup$
– EdOverflow
Jan 6 at 20:49
$begingroup$
what does bichromatic mean?
$endgroup$
– nafhgood
Jan 7 at 1:05
$begingroup$
@mathnoob I added an explanation
$endgroup$
– Erel Segal-Halevi
Jan 7 at 3:53
$begingroup$
@EdOverflow I found this expression here: arxiv.org/pdf/1810.06704.pdf If I understand correctly, it refers to coloring in which only some of the vertices are colored, while others are not colored at all.
$endgroup$
– Erel Segal-Halevi
Jan 7 at 4:18
$begingroup$
@erel-segal-halevi, yes, although the bichromatic property still holds for those that are coloured. I think the only downside to the term I suggested is that it implies the remaining vertices are not coloured at all (or not necessarily coloured). Maybe you could combine the termsproper colouringandsubgraphsto describe what you are after above. I would need to look into this a bit more before I can suggest a more concrete term.
$endgroup$
– EdOverflow
Jan 7 at 19:08
$begingroup$
"
Partial proper colouring", maybe?$endgroup$
– EdOverflow
Jan 6 at 20:49
$begingroup$
"
Partial proper colouring", maybe?$endgroup$
– EdOverflow
Jan 6 at 20:49
$begingroup$
what does bichromatic mean?
$endgroup$
– nafhgood
Jan 7 at 1:05
$begingroup$
what does bichromatic mean?
$endgroup$
– nafhgood
Jan 7 at 1:05
$begingroup$
@mathnoob I added an explanation
$endgroup$
– Erel Segal-Halevi
Jan 7 at 3:53
$begingroup$
@mathnoob I added an explanation
$endgroup$
– Erel Segal-Halevi
Jan 7 at 3:53
$begingroup$
@EdOverflow I found this expression here: arxiv.org/pdf/1810.06704.pdf If I understand correctly, it refers to coloring in which only some of the vertices are colored, while others are not colored at all.
$endgroup$
– Erel Segal-Halevi
Jan 7 at 4:18
$begingroup$
@EdOverflow I found this expression here: arxiv.org/pdf/1810.06704.pdf If I understand correctly, it refers to coloring in which only some of the vertices are colored, while others are not colored at all.
$endgroup$
– Erel Segal-Halevi
Jan 7 at 4:18
$begingroup$
@erel-segal-halevi, yes, although the bichromatic property still holds for those that are coloured. I think the only downside to the term I suggested is that it implies the remaining vertices are not coloured at all (or not necessarily coloured). Maybe you could combine the terms
proper colouring and subgraphs to describe what you are after above. I would need to look into this a bit more before I can suggest a more concrete term.$endgroup$
– EdOverflow
Jan 7 at 19:08
$begingroup$
@erel-segal-halevi, yes, although the bichromatic property still holds for those that are coloured. I think the only downside to the term I suggested is that it implies the remaining vertices are not coloured at all (or not necessarily coloured). Maybe you could combine the terms
proper colouring and subgraphs to describe what you are after above. I would need to look into this a bit more before I can suggest a more concrete term.$endgroup$
– EdOverflow
Jan 7 at 19:08
|
show 1 more comment
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$begingroup$
"
Partial proper colouring", maybe?$endgroup$
– EdOverflow
Jan 6 at 20:49
$begingroup$
what does bichromatic mean?
$endgroup$
– nafhgood
Jan 7 at 1:05
$begingroup$
@mathnoob I added an explanation
$endgroup$
– Erel Segal-Halevi
Jan 7 at 3:53
$begingroup$
@EdOverflow I found this expression here: arxiv.org/pdf/1810.06704.pdf If I understand correctly, it refers to coloring in which only some of the vertices are colored, while others are not colored at all.
$endgroup$
– Erel Segal-Halevi
Jan 7 at 4:18
$begingroup$
@erel-segal-halevi, yes, although the bichromatic property still holds for those that are coloured. I think the only downside to the term I suggested is that it implies the remaining vertices are not coloured at all (or not necessarily coloured). Maybe you could combine the terms
proper colouringandsubgraphsto describe what you are after above. I would need to look into this a bit more before I can suggest a more concrete term.$endgroup$
– EdOverflow
Jan 7 at 19:08