# Tagged Questions

49 views

### Count of all simple paths between two vertices in a Complete graph [closed]

A path is simple if it repeats no vertices. How many simple paths between two vertices in Complete graph? One way is listing the simple paths is to use depth-first search. but i think it should be ...
82 views

### number of edges in a graph

I got a problem related to graph theory - Consider an undirected graph ܩ where self-loops are not allowed. The vertex set of G is {(i,j):1<=i,j <=12}. There is an edge between (a, b) and (c, ...
58 views

### Number of Matchings in a Bipartite

Given two sets A and B of sizes |A| = n and |B| = m, where m >= n. There are edges from set A to set B. I need to find the number of matchings where all of vertices ...
135 views

### Bipartite Graph Game

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 ...
194 views

### Team construction in tri-partite graph

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 ...