Homework Answers
QUESTION 6
We know that, every tree is a bipartite graph. Also, the chromatic number of a bipartite graph is 2. Clearly, the chromatic number of any tree is 2.
QUESTION 7
We have , the chromatic number of Kn is n.
Then, the chromatic number of K7 is 7.
QUESTION 8
The smallest number of colours needed to properly colour the vertices of a graph is it's chromatic number.
Again , we know that, K3,4 is a complete bipartite graph.
Also, the chromatic number of a bipartite graph is 2.
So, the chromatic number of K3,4 is 2.
Thus, smallest number of colours needed to properly colour the vertices of K3,4 is 2.
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QUESTION 6 What is the chromatic number of any tree? QUESTION 7 What is the chromatic...
Translate psuedo code for computing chromatic number of a grapgh to java code 1 //graph G,...
Translate psuedo code for computing chromatic number of a grapgh to
java code
1 //graph G, vertices n, vertices are numbered o,1-- //G i //colors are stored in arrayq //qlil has color of vertex i, initially all0 s stored in adjacency list or adjacency matrix p , returns chromatic number //colors G using mininum number of colors int color () for (i 1 to n) //if G can be colored using i colors starting at vertex 0 if (color (0,...
he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1 he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1
he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1
he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1
Show all work for full credit. PART A Graph Theorv). 01.a. Model the following problem into a graph coloring problem A local zoo wants to take visitors on animal feeding tours, and is consider...
Show all work for full credit. PART A Graph Theorv). 01.a. Model the following problem into a graph coloring problem A local zoo wants to take visitors on animal feeding tours, and is considering the following tours: Tour 1 visits the monkeys, birds, and deer Tour 2 visits the elephants, deer and giraffes; Tour 3 visits the birds, reptiles and bears Tour 4 visits the kangaroos, monkeys and bears Tour 5 visits birds, kangaroos and pandas; Monday, Wednesday and Friday...
show all the work a9) What is meant by coloring the vertices of a graph? Define the chromatic number of a graph. a) What is the famous 4- color theorem? b) Translate the following map into a graph...
show all the work
a9) What is meant by coloring the vertices of a graph? Define the chromatic number of a graph. a) What is the famous 4- color theorem? b) Translate the following map into a graph G and find χ (G). You may draw G embedded in the map or alongside the map. No need to consider the outside region. 了 jo
a9) What is meant by coloring the vertices of a graph? Define the chromatic number of...
2 A) B) C) What is the chromatic number of the 9-cycle C,? What is the...
2
A)
B)
C)
What is the chromatic number of the 9-cycle C,? What is the chromatic number of the complete bipartite graph K3,3? What is the chromatic number of the complete graph Ky?
Problem 12.29. A basic example of a simple graph with chromatic number n is the complete graph on...
Problem 12.29. A basic example of a simple graph with chromatic number n is the complete graph on n vertices, that is x(Kn) n. This implies that any graph with Kn as a subgraph must have chromatic number at least n. It's a common misconception to think that, conversely, graphs with high chromatic number must contain a large complete sub- graph. In this problem we exhibit a simple example countering this misconception, namely a graph with chromatic number four that...
QUESTION 9 Find the chromatic number of the graph below. QUESTION 10 What is the chromatic...
QUESTION 9 Find the chromatic number of the graph below. QUESTION 10 What is the chromatic number of the graph below?
Prove that in any tree with n vertices, the number of nodes with degree 8 or...
Prove that in any tree with n vertices, the number of nodes with degree 8 or more is at most (n − 1)/4.
this is a discrete math 2. What is the minimum number of colors needed to color...
this is a discrete math
2. What is the minimum number of colors needed to color the vertices of this graph? Color the vertices with this minimum number of colors.
Write the number of colors needed to color the vertices of each graph or object listed....
Write the number of colors needed to color the vertices of each graph or object listed. (You should not need to draw them.) KS Any 2-dimensional map КА
Translate psuedo code for computing chromatic number of a grapgh to
java code
1 //graph G, vertices n, vertices are numbered o,1-- //G i //colors are stored in arrayq //qlil has color of vertex i, initially all0 s stored in adjacency list or adjacency matrix p , returns chromatic number //colors G using mininum number of colors int color () for (i 1 to n) //if G can be colored using i colors starting at vertex 0 if (color (0,...
he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1
he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1
Show all work for full credit. PART A Graph Theorv). 01.a. Model the following problem into a graph coloring problem A local zoo wants to take visitors on animal feeding tours, and is considering the following tours: Tour 1 visits the monkeys, birds, and deer Tour 2 visits the elephants, deer and giraffes; Tour 3 visits the birds, reptiles and bears Tour 4 visits the kangaroos, monkeys and bears Tour 5 visits birds, kangaroos and pandas; Monday, Wednesday and Friday...
show all the work
a9) What is meant by coloring the vertices of a graph? Define the chromatic number of a graph. a) What is the famous 4- color theorem? b) Translate the following map into a graph G and find χ (G). You may draw G embedded in the map or alongside the map. No need to consider the outside region. 了 jo
a9) What is meant by coloring the vertices of a graph? Define the chromatic number of...
2
A)
B)
C)
What is the chromatic number of the 9-cycle C,? What is the chromatic number of the complete bipartite graph K3,3? What is the chromatic number of the complete graph Ky?
Problem 12.29. A basic example of a simple graph with chromatic number n is the complete graph on n vertices, that is x(Kn) n. This implies that any graph with Kn as a subgraph must have chromatic number at least n. It's a common misconception to think that, conversely, graphs with high chromatic number must contain a large complete sub- graph. In this problem we exhibit a simple example countering this misconception, namely a graph with chromatic number four that...
QUESTION 9 Find the chromatic number of the graph below. QUESTION 10 What is the chromatic number of the graph below?
this is a discrete math
2. What is the minimum number of colors needed to color the vertices of this graph? Color the vertices with this minimum number of colors.
Write the number of colors needed to color the vertices of each graph or object listed. (You should not need to draw them.) KS Any 2-dimensional map КА
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