Prove that g is bipartite with parts x and y

Reference no: EM131165724

Let G be a connected graph with no odd cycles. Let x beavertex of G. Let X be all vertices at an even distance from x, and let Y be all vertices at an odd distance from x. Prove that G is bipartite with parts X and Y.

Reference no: EM131165724

Questions Cloud

For which values of m and n is km n hamiltonian : The complete bipartite graph Km,n is a graph with m + n vertices. These vertices are divided into a set of size m and a set of size n. We call these sets the parts of the graph. Within each of these sets there are no edges. But between each pair o..

Federal reserve would increase the money supply : Explain the 4 ways the Federal Reserve would increase the money Supply and explain and graph how this would impact interest rates, consumption, investment, AD, GDP, Prices and Unemployment. Calculate and graph (both the money and goods graph) what wo..

Incentive plans work only for a relatively short time : It has been said that incentive plans work only for a relatively short time. - Do you agree or disagree? - Why?

Draw her labor-leisure budget constraint : Tamara earns $8 an hour and works 60 hours/week. Draw her labor-leisure budget constraint. What determines its slope? How does the position and slope of her budget constraint change if her wage increases to $16 per hour?

Prove that g is bipartite with parts x and y : Let G be a connected graph with no odd cycles. Let x beavertex of G. Let X be all vertices at an even distance from x, and let Y be all vertices at an odd distance from x. Prove that G is bipartite with parts X and Y.

Would you choose an individual or a group : If you were able to choose the type of incentive pay system your company offered, would you choose an individual, a group, or an organization wide incentive plan? Why?

What is the sum of the maximum size of an independent set : What is the sum of the maximum size of an independent set and the minimum size of a vertex cover in a graph G? Hint: it is useful to think both about the independent set and its complement (relative to the vertex set).

What level of profits will each firm actually earn : Assuming both firms pursue a safe strategy, what strategy will each firm pursue and what level of profits will each firm actually earn? Make sure to reference the payoff matrix in your answer

Planning a survey deployed via the internet : What should we consider in planning a survey deployed via the Internet? What challenges might we face in sending the survey instrument to all employees?

User Account

All Pages