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Path of given length in a rectangle
$begingroup$
I'm trying to make a path of given length in a rectangle divided onto $ncdot m$ nodes.
$n=2, m=5$ rectangle looks like this:
. . . . .
. . . . .
And I can cut out of any node. (I can move only vertically or horizontally and I need to get from the top left corner to the bottom right one in $k$ steps). Solution for $k=8$ is this:
. # . . .
. . . # .
My questions are:
1) Which lengths $k$ are possible in $ncdot m$ rectangle?
2) How can I find these routes/which nodes do I cut out?
graph-theory
asked Jan 19 at 12:59
LipovlanLipovlan
134
$endgroup$
add a comment |
$begingroup$
I'm trying to make a path of given length in a rectangle divided onto $ncdot m$ nodes.
$n=2, m=5$ rectangle looks like this:
. . . . .
. . . . .
And I can cut out of any node. (I can move only vertically or horizontally and I need to get from the top left corner to the bottom right one in $k$ steps). Solution for $k=8$ is this:
. # . . .
. . . # .
My questions are:
1) Which lengths $k$ are possible in $ncdot m$ rectangle?
2) How can I find these routes/which nodes do I cut out?
graph-theory
asked Jan 19 at 12:59
LipovlanLipovlan
134
$endgroup$
add a comment |
$begingroup$
I'm trying to make a path of given length in a rectangle divided onto $ncdot m$ nodes.
$n=2, m=5$ rectangle looks like this:
. . . . .
. . . . .
And I can cut out of any node. (I can move only vertically or horizontally and I need to get from the top left corner to the bottom right one in $k$ steps). Solution for $k=8$ is this:
. # . . .
. . . # .
My questions are:
1) Which lengths $k$ are possible in $ncdot m$ rectangle?
2) How can I find these routes/which nodes do I cut out?
graph-theory
asked Jan 19 at 12:59
LipovlanLipovlan
134
$endgroup$
I'm trying to make a path of given length in a rectangle divided onto $ncdot m$ nodes.
$n=2, m=5$ rectangle looks like this:
. . . . .
. . . . .
And I can cut out of any node. (I can move only vertically or horizontally and I need to get from the top left corner to the bottom right one in $k$ steps). Solution for $k=8$ is this:
. # . . .
. . . # .
My questions are:
1) Which lengths $k$ are possible in $ncdot m$ rectangle?
2) How can I find these routes/which nodes do I cut out?
graph-theory
graph-theory
asked Jan 19 at 12:59
LipovlanLipovlan
134
asked Jan 19 at 12:59
LipovlanLipovlan
134
asked Jan 19 at 12:59
LipovlanLipovlan
134
asked Jan 19 at 12:59
LipovlanLipovlan
134
asked Jan 19 at 12:59
LipovlanLipovlan
134
134
add a comment |
add a comment |
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