Coloring a Cycle Graph

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Cycle:- cycle is a path of edges and vertices wherein a vertex is reachable from itself. or in other words, it is a Closed walk.

Even Cycle:- In which Even number of vertices is present is known as Even Cycle.

Odd Cycle:- In which Odd number of Vertices is present is known as Odd Cycle.
Given the number of vertices in a Cyclic Graph. The task is to determine the Number of colors required to color the graph so that No two Adjacent vertices have the same color.

Approach:

If the no. of vertices is Even then it is Even Cycle and to color such graph we require 2 colors.
If the no. of vertices is Odd then it is Odd Cycle and to color such graph we require 3 colors.

Examples:

Input : vertices = 3
Output : No. of colors require is: 3

Input : vertices = 4
Output : No. of colors require is: 2

Example 1: Even Cycle: Number of vertices = 4

Color required = 2

Example 2: Odd Cycle: Number of vertices = 5

Color required = 3

Implementation:

C++

// CPP program to find number of colors
// required to color a cycle graph
#include <bits/stdc++.h>
using namespace std;
 
// Function that calculates Color
// require to color a graph.
int Color(int vertices)
{
    int result = 0;
 
    // Check if number of vertices
    // is odd or even.
    // If number of vertices is even
    // then color require is 2 otherwise 3
    if (vertices % 2 == 0)
        result = 2;
    else
        result = 3;
 
    return result;
}
 
// Driver code
int main()
{
    int vertices = 3;
    cout << "No. of colors require is: " << Color(vertices);
    return 0;
}

Java

// Java program to find number of colors
// required to color a cycle graph
import java.io.*; 
 
class GFG { 
   
    // Function that calculates Color 
    // require to color a graph.  
    static int Color(int vertices) 
    { 
        int result = 0; 
   
        // Check if number of vertices 
        // is odd or even. 
        // If number of vertices is even 
        // then color require is 2 otherwise 3 
        if (vertices % 2 == 0) 
            result = 2; 
        else
            result = 3; 
       
        return result; 
    }  
       
    // Driver program to test above function 
    public static void main (String[] args) 
    { 
        int vertices = 3; 
         
        System.out.println("No. of colors require is: " + Color(vertices));
           
    } 
} 
 
// this code is contributed by Naman_Garg

Python3

# Naive Python3 Program to 
# find the number of colors
# required to color a cycle graph  
   
# Function to find Color required.
def Color(vertices):  
   
    result = 0
   
    # Check if number of vertices 
    # is odd or even. 
    # If number of vertices is even 
    # then color require is 2 otherwise 3 
    if (vertices % 2 == 0):
        result = 2
    else:
        result = 3
   
    return result
   
# Driver Code 
if __name__=='__main__':
    vertices = 3
    print ("No. of colors require is:",Color(vertices))
 
# this code is contributed by Naman_Garg

C#

// C# program to find number of colors
// required to color a cycle graph
using System; 
 
class GFG
{ 
 
// Function that calculates Color 
// require to color a graph. 
static int Color(int vertices) 
{ 
    int result = 0; 
 
    // Check if number of vertices 
    // is odd or even. 
    // If number of vertices is even 
    // then color require is 2 otherwise 3 
    if (vertices % 2 == 0) 
        result = 2; 
    else
        result = 3; 
 
    return result; 
} 
 
// Driver Code
public static void Main () 
{ 
    int vertices = 3; 
     
    Console.WriteLine("No. of colors required is: " + 
                                   Color(vertices));
} 
} 
 
// This code is contributed by anuj_67

PHP

<?php
// PHP program to find number of colors
// required to color a cycle graph
 
// Function that calculates Color
// require to color a graph.
function Color($vertices)
{
    $result = 0;
 
    // Check if number of vertices
    // is odd or even.
    // If number of vertices is even
    // then color require is 2 otherwise 3
    if ($vertices % 2 == 0)
        $result = 2;
    else
        $result = 3;
 
    return $result;
}
 
// Driver code
$vertices = 3;
echo "No. of colors required is: " ,
                  Color($vertices);
 
// This code is contributed 
// by anuj_67
?>

Javascript

<script>
 
// Javascript program to find number of colors
// required to color a cycle graph
 
// Function that calculates Color
// require to color a graph.
function Color(vertices)
{
    var result = 0;
 
    // Check if number of vertices
    // is odd or even.
    // If number of vertices is even
    // then color require is 2 otherwise 3
    if (vertices % 2 == 0)
        result = 2;
    else
        result = 3;
 
    return result;
}
 
// Driver code
var vertices = 3;
document.write("No. of colors require is: " +
               Color(vertices));
                
// This code is contributed by itsok
 
</script>

Output

No. of colors require is: 3

Complexity Analysis:

Time Complexity: O(1)
Space Complexity: O(1)

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