connected subgraphs having minimum expansion
If I have a connected graph $G$, is it true that subgraphs(corresponding to cuts) having minimum conductance or expansion(or other connectivity measures) should be connected?
In other words if $S$ is a subgraph for which $phi(G) = |delta(S)|/|S| $ does this imply that $S$ and $V-S$ are connected?
NOTE: Assuming $S$ having at least two connected components (and $S_1$ one of them) I tried to use the connectedness of the graph to make cut $S' = S - S_1$ reduce the nominator of the fraction and controlling min(|S'|,|V_S'|) but it seems that this does't work!
graph-theory connectedness
asked Jan 4 at 18:21
DandelionDandelion
1299
add a comment |
If I have a connected graph $G$, is it true that subgraphs(corresponding to cuts) having minimum conductance or expansion(or other connectivity measures) should be connected?
In other words if $S$ is a subgraph for which $phi(G) = |delta(S)|/|S| $ does this imply that $S$ and $V-S$ are connected?
NOTE: Assuming $S$ having at least two connected components (and $S_1$ one of them) I tried to use the connectedness of the graph to make cut $S' = S - S_1$ reduce the nominator of the fraction and controlling min(|S'|,|V_S'|) but it seems that this does't work!
graph-theory connectedness
asked Jan 4 at 18:21
DandelionDandelion
1299
1
The answer is no. For example consider the star graphs.
– Mahdi
Jan 6 at 8:59
add a comment |
If I have a connected graph $G$, is it true that subgraphs(corresponding to cuts) having minimum conductance or expansion(or other connectivity measures) should be connected?
In other words if $S$ is a subgraph for which $phi(G) = |delta(S)|/|S| $ does this imply that $S$ and $V-S$ are connected?
NOTE: Assuming $S$ having at least two connected components (and $S_1$ one of them) I tried to use the connectedness of the graph to make cut $S' = S - S_1$ reduce the nominator of the fraction and controlling min(|S'|,|V_S'|) but it seems that this does't work!
graph-theory connectedness
asked Jan 4 at 18:21
DandelionDandelion
1299
If I have a connected graph $G$, is it true that subgraphs(corresponding to cuts) having minimum conductance or expansion(or other connectivity measures) should be connected?
In other words if $S$ is a subgraph for which $phi(G) = |delta(S)|/|S| $ does this imply that $S$ and $V-S$ are connected?
NOTE: Assuming $S$ having at least two connected components (and $S_1$ one of them) I tried to use the connectedness of the graph to make cut $S' = S - S_1$ reduce the nominator of the fraction and controlling min(|S'|,|V_S'|) but it seems that this does't work!
graph-theory connectedness
graph-theory connectedness
asked Jan 4 at 18:21
DandelionDandelion
1299
asked Jan 4 at 18:21
DandelionDandelion
1299
asked Jan 4 at 18:21
DandelionDandelion
1299
asked Jan 4 at 18:21
DandelionDandelion
1299
asked Jan 4 at 18:21
DandelionDandelion
1299
1299
1
The answer is no. For example consider the star graphs.
– Mahdi
Jan 6 at 8:59
add a comment |
1
The answer is no. For example consider the star graphs.
– Mahdi
Jan 6 at 8:59
1
1
The answer is no. For example consider the star graphs.
– Mahdi
Jan 6 at 8:59
The answer is no. For example consider the star graphs.
– Mahdi
Jan 6 at 8:59
add a comment |
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The answer is no. For example consider the star graphs.
– Mahdi
Jan 6 at 8:59