Homework Answers
Chromatic number is the minimum Number of colours needed to colour the vertices of the graph.
Chromatic number of graph Kn is n.
Hence the answers to the given questions are-
a) Colours needed for K4 = 4
b) Colours needed for K8 = 8
c) Colours needed to colour any 2-dimensional map = 4
Add Answer to:
Write the number of colors needed to color the vertices of each graph or object listed....
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.
Construct the dual graph for the map shown. Then, find the number of colors needed to color the map so that no two adja...
Construct the dual graph for the map shown. Then, find the number of colors needed to color the map so that no two adjacent regions have the same color. 4. a) b) CCE
Construct the dual graph for the map shown. Then, find the number of colors needed to color the map so that no two adjacent regions have the same color. 4. a) b) CCE
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...
You own n colors, and want to use them to color 6 objects. For each object,...
You own n colors, and want to use them to color 6 objects. For each object, you randomly choose one of the colors. How large does n have to be so that odds are that no two objects will have the same color (i.e., every object is colored in a different color)?
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices...
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle) Show that on n vertices, respectively. Nm(P N(C= (m - 1) (-1)"-1 (m 1)"-2)
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle)...
1. You own n colors, and want to use them to color 6 objects. For each...
1. You own n colors, and want to use them to color 6 objects. For each object, you randomly choose one of the colors. How large does n have to be so that odds are that no two objects will have the same color (i.e., every object is colored in a different color)? 2. Consider the following game: An urn contains 20 white balls and 10 black balls. If you draw a white ball, you get $1, but if you...
A 2-coloring of an undirected graph with n vertices and m edges is the assignment of one of two colors (say, red or green) to each vertex of the graph
A 2-coloring of an undirected graph with n vertices and m edges is the assignment of one of two colors (say, red or green) to each vertex of the graph, so that no two adjacent nodes have the same color. So, if there is an edge (u,v) in the graph, either node u is red and v is green or vice versa. Give an O(n + m) time algorithm (pseudocode!) to 2-colour a graph or determine that no such coloring...
2 (a) Draw the graphs K5,2 and K5,3 using the standard arrangement. For example, K5,2 should have a row of 5 vertices above a row of 2 vertices, and the edges connect each vertex in the top row to ea...
2 (a) Draw the graphs K5,2 and K5,3 using the standard
arrangement.
For example, K5,2 should have a row of 5 vertices above a row of
2 vertices, and the edges connect each vertex in the top row to
each vertex in the bottom row.
(b) Draw K5,2 as a plane graph, i.e., with no edges
crossing.
(c) Complete the following table, recalling E is the number of
edges in a graph and V is the number of vertices. (Strictly...
014) Draw a dual graph G for the following planar map, and find a coloring for the vertices of G that uses x(G) number of colors o cean Q15. Solve the following TSP problem 3 4 55305 302 320 C Usi...
014) Draw a dual graph G for the following planar map, and find a coloring for the vertices of G that uses x(G) number of colors o cean Q15. Solve the following TSP problem 3 4 55305 302 320 C Using the nearest neighbor algorithm., if A is the home city. Shade the edges used. Find the distance travelled. E x piaun the qlgor tam a) 340 305 30 D 320 С Using the sorted edge algorithm. Show work (...
Recall the definition of the degree of a vertex in a graph. a) Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph necessarily connected ? b) Now the graph has 7 vertices, each degree...
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
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.
Construct the dual graph for the map shown. Then, find the number of colors needed to color the map so that no two adjacent regions have the same color. 4. a) b) CCE
Construct the dual graph for the map shown. Then, find the number of colors needed to color the map so that no two adjacent regions have the same color. 4. a) b) CCE
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...
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle) Show that on n vertices, respectively. Nm(P N(C= (m - 1) (-1)"-1 (m 1)"-2)
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle)...
1. You own n colors, and want to use them to color 6 objects. For each object, you randomly choose one of the colors. How large does n have to be so that odds are that no two objects will have the same color (i.e., every object is colored in a different color)? 2. Consider the following game: An urn contains 20 white balls and 10 black balls. If you draw a white ball, you get $1, but if you...
2 (a) Draw the graphs K5,2 and K5,3 using the standard
arrangement.
For example, K5,2 should have a row of 5 vertices above a row of
2 vertices, and the edges connect each vertex in the top row to
each vertex in the bottom row.
(b) Draw K5,2 as a plane graph, i.e., with no edges
crossing.
(c) Complete the following table, recalling E is the number of
edges in a graph and V is the number of vertices. (Strictly...
014) Draw a dual graph G for the following planar map, and find a coloring for the vertices of G that uses x(G) number of colors o cean Q15. Solve the following TSP problem 3 4 55305 302 320 C Using the nearest neighbor algorithm., if A is the home city. Shade the edges used. Find the distance travelled. E x piaun the qlgor tam a) 340 305 30 D 320 С Using the sorted edge algorithm. Show work (...
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
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