Given a X(G) coloring of the graph G, is it possible to find every other possible X(G)-coloring of G?
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Given a coloring of the graph $G$ using $chi(G)$ (the chromatic number of $G$) colors is it possible to find every other $chi(G)$-coloring of $G$? One way of finding other $chi(G)$-coloring of $G$ is by swapping 2 or more colors from the given coloring of $G$, an other way is by using Kempe chain recoloring. Are those two way of recoloring going to give me every possible $chi(G)$-coloring of $G$? Is there a proof or a counter-proof to it? Is there other ways of recoloring without increasing the number of color used?
graph-theory coloring
edited Nov 20 at 1:10
mathnoob
1,133115
asked Nov 6 '16 at 11:16
Andrea Nardi
62
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up vote
1
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Given a coloring of the graph $G$ using $chi(G)$ (the chromatic number of $G$) colors is it possible to find every other $chi(G)$-coloring of $G$? One way of finding other $chi(G)$-coloring of $G$ is by swapping 2 or more colors from the given coloring of $G$, an other way is by using Kempe chain recoloring. Are those two way of recoloring going to give me every possible $chi(G)$-coloring of $G$? Is there a proof or a counter-proof to it? Is there other ways of recoloring without increasing the number of color used?
graph-theory coloring
edited Nov 20 at 1:10
mathnoob
1,133115
asked Nov 6 '16 at 11:16
Andrea Nardi
62
Is the graph connected?
– bof
Nov 20 at 3:26
What about the "friendship graph" $F_n$?
– bof
Nov 20 at 3:27
@bof Yes, the graph is connected. I think that even if a graph is not connected, a method can be inferred by analyzing each connected component of the graph individually.
– Andrea Nardi
Nov 20 at 14:03
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Given a coloring of the graph $G$ using $chi(G)$ (the chromatic number of $G$) colors is it possible to find every other $chi(G)$-coloring of $G$? One way of finding other $chi(G)$-coloring of $G$ is by swapping 2 or more colors from the given coloring of $G$, an other way is by using Kempe chain recoloring. Are those two way of recoloring going to give me every possible $chi(G)$-coloring of $G$? Is there a proof or a counter-proof to it? Is there other ways of recoloring without increasing the number of color used?
graph-theory coloring
edited Nov 20 at 1:10
mathnoob
1,133115
asked Nov 6 '16 at 11:16
Andrea Nardi
62
Given a coloring of the graph $G$ using $chi(G)$ (the chromatic number of $G$) colors is it possible to find every other $chi(G)$-coloring of $G$? One way of finding other $chi(G)$-coloring of $G$ is by swapping 2 or more colors from the given coloring of $G$, an other way is by using Kempe chain recoloring. Are those two way of recoloring going to give me every possible $chi(G)$-coloring of $G$? Is there a proof or a counter-proof to it? Is there other ways of recoloring without increasing the number of color used?
graph-theory coloring
graph-theory coloring
edited Nov 20 at 1:10
mathnoob
1,133115
asked Nov 6 '16 at 11:16
Andrea Nardi
62
edited Nov 20 at 1:10
mathnoob
1,133115
asked Nov 6 '16 at 11:16
Andrea Nardi
62
edited Nov 20 at 1:10
mathnoob
1,133115
edited Nov 20 at 1:10
mathnoob
1,133115
edited Nov 20 at 1:10
mathnoob
1,133115
1,133115
asked Nov 6 '16 at 11:16
Andrea Nardi
62
asked Nov 6 '16 at 11:16
Andrea Nardi
62
asked Nov 6 '16 at 11:16
Andrea Nardi
62
62
Is the graph connected?
– bof
Nov 20 at 3:26
What about the "friendship graph" $F_n$?
– bof
Nov 20 at 3:27
@bof Yes, the graph is connected. I think that even if a graph is not connected, a method can be inferred by analyzing each connected component of the graph individually.
– Andrea Nardi
Nov 20 at 14:03
add a comment |
Is the graph connected?
– bof
Nov 20 at 3:26
What about the "friendship graph" $F_n$?
– bof
Nov 20 at 3:27
@bof Yes, the graph is connected. I think that even if a graph is not connected, a method can be inferred by analyzing each connected component of the graph individually.
– Andrea Nardi
Nov 20 at 14:03
Is the graph connected?
– bof
Nov 20 at 3:26
Is the graph connected?
– bof
Nov 20 at 3:26
What about the "friendship graph" $F_n$?
– bof
Nov 20 at 3:27
What about the "friendship graph" $F_n$?
– bof
Nov 20 at 3:27
@bof Yes, the graph is connected. I think that even if a graph is not connected, a method can be inferred by analyzing each connected component of the graph individually.
– Andrea Nardi
Nov 20 at 14:03
@bof Yes, the graph is connected. I think that even if a graph is not connected, a method can be inferred by analyzing each connected component of the graph individually.
– Andrea Nardi
Nov 20 at 14:03
add a comment |
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Is the graph connected?
– bof
Nov 20 at 3:26
What about the "friendship graph" $F_n$?
– bof
Nov 20 at 3:27
@bof Yes, the graph is connected. I think that even if a graph is not connected, a method can be inferred by analyzing each connected component of the graph individually.
– Andrea Nardi
Nov 20 at 14:03