This looks very similar to a 45 degree rotated board of the Bridg-it game: http://www.sites4all.co.uk/bridjit/ (About the winning strategy, see also https://en.wikipedia.org/wiki/Shannon_switching_game.)

But I really don't see how the existence of no draw (<=> there is a through path) would imply the same in your case. Of course in your example there can also be two through paths.

This looks very similar to a 45 degree rotated board of the so-called Bridg-it game. About the winning strategy, see https://en.wikipedia.org/wiki/Shannon_switching_game.

But I really don't see how the existence of no draw (<=> there is a through path) would imply the same in your case. Of course in your example there can also be two through paths.

This looks very similar to a 45 degree rotated board of the Bridg-it game: http://www.sites4all.co.uk/bridjit/ (About the winning strategy, see also http://en.wikipedia.org/wiki/Shannon_switching_game.)

But I really don't see how the existence of no draw (<=> there is a through path) would imply the same in your case. Of course in your example there can also be two through paths.

This looks very similar to a 45 degree rotated board of the Bridg-it game: http://www.sites4all.co.uk/bridjit/ (About the winning strategy, see also https://en.wikipedia.org/wiki/Shannon_switching_game.)

But I really don't see how the existence of no draw (<=> there is a through path) would imply the same in your case. Of course in your example there can also be two through paths.