So say we have a bipartite graph G=(X,Y,E). Let's make a game out of it. I go first. I pick a node in X. You go next. You pick a node in Y that is connected by an edge to the node I picked. Next it's ...
The government wants to create a team with one alchemist, one builder, and one computer-scientist. In order to have good cooperation, it is important that the 3 team-members like each other. ...
If a graph $G$ is connected and has no path with a length greater than $k$, prove that every two paths in $G$ of length $k$ have at least one vertex in common. I think that that common vertex ...
A unipathic graph is a directed graph such that there is at most one simple path from any one vertex to any other vertex. Unipathic graphs can have cycles. For example, a doubly linked list (not a ...