## How many Colours are used in a bipartite graph?

3. How many colours are used in a bipartite graph? Explanation: A bipartite graph is said to be two-colourable so that every edge has its vertices coloured in different colours.

**What is the condition for proper Colouring of a graph?**

Explanation: The condition for proper coloring of graph is that two vertices which share a common edge should not have the same color. If it uses k colors in the process then it is called k coloring of graph.

**Is a bipartite graph connected?**

bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. A bipartite graph doesn’t need to be connected.

### How many Colours are used in a bipartite graph Mcq?

Explanation: A bipartite graph is a graph such that no two vertices of the same set are adjacent to each other. So the number of unique colors required for proper coloring of the graph will be 2.

**How do you prove a bipartite graph?**

The graph is a bipartite graph if:

- The vertex set of can be partitioned into two disjoint and independent sets and.
- All the edges from the edge set have one endpoint vertex from the set and another endpoint vertex from the set.

**How do you know if a bipartite graph is connected?**

A graph is bipartite if and only if it does not contain an odd cycle. A graph is bipartite if and only if it is 2-colorable, (i.e. its chromatic number is less than or equal to 2).

#### What makes a graph bipartite?

A Bipartite Graph is a graph whose vertices can be divided into two independent sets, U and V such that every edge (u, v) either connects a vertex from U to V or a vertex from V to U.

**What is a graph coloring and how is it applied?**

Graph coloring is the procedure of assignment of colors to each vertex of a graph G such that no adjacent vertices get same color. The objective is to minimize the number of colors while coloring a graph. The smallest number of colors required to color a graph G is called its chromatic number of that graph.

**Can a bipartite graph be colored with two colors?**

A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color. Note that it is possible to color a cycle graph with even cycle using two colors.

## What is a connected component in a graph?

A set of nodes forms a connected component in an undirected graph if any node from the set of nodes can reach any other node by traversing edges. The main point here is reachability. In connected components, all the nodes are always reachable from each other.

**How many different colours are used to illustrate connected components?**

We used four different colours to illustrate the connected components in , namely: , , , . 7. Time Complexity Analysis The algorithm we just saw for finding connected components in a given undirected graph uses the DFS search and counts the number of calls to the DFS function.

**How to find if a graph is bipartite using BFS?**

Following is a simple algorithm to find out whether a given graph is Bipartite or not using Breadth First Search (BFS). 1. Assign RED color to the source vertex (putting into set U). 2. Color all the neighbors with BLUE color (putting into set V).