Rules

Alice and Bob take turns claiming territories on a map with a finite number of territories. After their first turn, a player may only claim a territory if it borders one they already own. If a player has no moves available, they lose their turn. Once neither player can move, a player wins if they own more territories.

Examples

On the map below, play might proceed as follows:

1. Alice claims B,
2. Bob claims C,
3. Alice claims A,
4. Bob claims D,

resulting in a 2-2 draw.

On this map, here's how the game might go:

1. Alice claims B,
2. Bob claims C,
3. Alice claims D,
4. Bob loses his turn,
5. Alice claims A,

and Alice wins 3-1.

Question

It's possible for Bob to win on both of the maps shown, but only if Alice makes a mistake; if she plays correctly, she wins or draws as demonstrated.

Is there a map where Bob can guarantee a win?