MathDB

Baron and Peter are playing a game. They are given a simple finite graph

G

with

n\ge 3

vertex and

k

edges that connects the vertices. First Peter labels two vertices A and B, and places a counter at A. Baron starts first. A move for Baron is move the counter along an edge. Peter's move is to remove an edge from the graph. Baron wins if he reaches

B

, otherwise Peter wins.
Given the value of

n

, what is the largest

k

so that Peter can always win?

Problem Statement