For any m × n grid graph with m rows of n vertices, Find the greatest length of any path in such a graph.

[oofiedoofie]

For any m × n grid graph with m rows of n vertices, Find the greatest length of any path in such a graph.
Let m, n ≥ 2
A path is where no vertices or no edges are repeated.

 

[MaxMath]

What do you mean by longest? Is it the most number of edges, or sum of lengths of edges, or anything else. I presume edges are not weighed.

In the former case, it appears that a party that traverses all vertices will necessarily be the longest, correct? Are crossings allowed? Presumably not.

 

[pka]

For any m × n grid graph with m rows of n vertices, Find the greatest length of any path in such a graph.
Let m, n ≥ 2
A path is where no vertices or no edges are repeated.

@oofiefie, in graph theory an [imath]m\times n[/imath] grid is a very particular graph.
It is a rectangular array of vertices in which the longest path moves [imath](0,0)\to(m,n)[/imath].
We move [imath]{\bf m}\text { places to the right and }{\bf n} \text{ places to the up}[/imath] never left nor down.
Please review to make sure that is what you meant.
GRAPHS An Introduction on the used book market.


[imath][/imath][imath][/imath][imath][/imath]

 

[DerrickOlley]

@oofiefie, in graph theory an [imath]m\times n[/imath] grid is a very particular graph.
It is a rectangular array of vertices in which the longest path moves [imath](0,0)\to(m,n)[/imath].
We move [imath]{\bf m}\text { places to the right and }{\bf n} \text{ places to the up}[/imath] never left nor down.Here.
Please review to make sure that is what you meant.
GRAPHS An Introduction on the used book market.


[imath][/imath][imath][/imath][imath][/imath]

Had a similar problem! And the book is just cool, I have been looking for it for a long time!