Let K(2,3) have bipartition B⋃W where B={a,b} and W={x,y,z}
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Why in a spanning tree of K(2,3) there must be precisely one of the vertices of {x,y,z} joined to both "a" and "b" ?
graph-theory bipartite-graph
asked Nov 16 at 11:19
Yahya
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Why in a spanning tree of K(2,3) there must be precisely one of the vertices of {x,y,z} joined to both "a" and "b" ?
graph-theory bipartite-graph
asked Nov 16 at 11:19
Yahya
175
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Why in a spanning tree of K(2,3) there must be precisely one of the vertices of {x,y,z} joined to both "a" and "b" ?
graph-theory bipartite-graph
asked Nov 16 at 11:19
Yahya
175
Why in a spanning tree of K(2,3) there must be precisely one of the vertices of {x,y,z} joined to both "a" and "b" ?
graph-theory bipartite-graph
graph-theory bipartite-graph
asked Nov 16 at 11:19
Yahya
175
asked Nov 16 at 11:19
Yahya
175
asked Nov 16 at 11:19
Yahya
175
asked Nov 16 at 11:19
Yahya
175
asked Nov 16 at 11:19
Yahya
175
175
add a comment |
add a comment |
1 Answer
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A spanning tree contains all vertices, but there is no edge between $a$ and $b$, so at least one vertex of $W$ must be connected to both.
If they were connected to 2 vertices from $W$, it would contain a circle.
answered Nov 16 at 11:29
Berci
59.2k23671
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
A spanning tree contains all vertices, but there is no edge between $a$ and $b$, so at least one vertex of $W$ must be connected to both.
If they were connected to 2 vertices from $W$, it would contain a circle.
answered Nov 16 at 11:29
Berci
59.2k23671
add a comment |
up vote
0
down vote
accepted
A spanning tree contains all vertices, but there is no edge between $a$ and $b$, so at least one vertex of $W$ must be connected to both.
If they were connected to 2 vertices from $W$, it would contain a circle.
answered Nov 16 at 11:29
Berci
59.2k23671
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
A spanning tree contains all vertices, but there is no edge between $a$ and $b$, so at least one vertex of $W$ must be connected to both.
If they were connected to 2 vertices from $W$, it would contain a circle.
answered Nov 16 at 11:29
Berci
59.2k23671
A spanning tree contains all vertices, but there is no edge between $a$ and $b$, so at least one vertex of $W$ must be connected to both.
If they were connected to 2 vertices from $W$, it would contain a circle.
answered Nov 16 at 11:29
Berci
59.2k23671
answered Nov 16 at 11:29
Berci
59.2k23671
answered Nov 16 at 11:29
Berci
59.2k23671
answered Nov 16 at 11:29
Berci
59.2k23671
59.2k23671
add a comment |
add a comment |
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