Testing Bipartiteness solved by 612

Problem

Figure 1. The graphs from the dataset

A bipartite graph is a graph $G = (V, E)$ whose vertices can be partitioned into two sets ($V = V_1 \cup V_2$ and $V_1 \cap V_2 = \emptyset$) such that there are no edges between vertices in the same set (for instance, if $u, v \in V_1$, then there is no edge between $u$ and $v$).

There are many other ways to formulate this property. For instance, an undirected graph is bipartite if and only if it can be colored with just two colors. Another one: an undirected graph is bipartite if and only if it contains no cycles of odd length.

Source: Algorithms by Dasgupta, Papadimitriou, Vazirani. McGraw-Hill. 2006.

Given: A positive integer $k \le 20$ and $k$ simple graphs in the edge list format with at most $10^3$ vertices each.

Return: For each graph, output "1" if it is bipartite and "-1" otherwise.

See Figure 1 for visual example from the sample dataset.

Sample Dataset

2

3 3
1 2
3 2
3 1

4 3
1 4
3 1
1 2

Sample Output

-1 1