The Shortest Path
No Euler Tour?
In the previous chapter we considered the problem of finding Euler walks
and Euler tours.
We have theorems which determine whether a given connected graph has
Euler walks or Euler tours.
If it has an Euler walk or Euler
Hamiltonian Tour
Smart Decisions
In the previous chapter we considered the problem of finding Euler walks
and Euler tours. When the graph does not have Euler walks or Euler tours
we eulerize the graph.
Moreover, for weighted graphs we considered the pro
Machine Scheduling
Smart Decisions
In the previous chapter we considered the bin-packing problem. i.e., we
put boards into bins, and we want to find an optimal way to do this, i.e.,
we minimizes the number of bins needed to use.
In this chapter we consi
Spanning Tree
Smart Decisions
In chapter 3 we saw that the complexity of solving the minimum cost
Hamiltonian problems, i.e., find the Hamiltonian tour on a graph, by
the Brute-force approach is O(n!). Although there are faster methods
whose complexity i
Task Scheduling
Smart Decisions
In the previous chapters we considered some real-life problems and formulated in terms of mathematics, especially graph theory. For example we
considered finding Euler walks (tours), Hamiltonian tours, shortest paths
and s
Graph Coloring
Smart Decisions
In this chapter we study a seemingly unrelated problem with graph theory.
We study the map-coloring problem, i.e., given a map, we assign a color to
a country. The adjacent countries cannot be assigned by the same color.
Bipartite Graph
Smart Decisions
In the final chapter we consider the problem called matching in graph
theory.
In here matching can mean finding boyfriend/girlfriend, jobs, etc.
Lets consider an example to get a sense.
An Example: Marriage Problem
Give
Recovering DNA
Smart Decisions
In this chapter we will see how Euler tours and Hamiltonian tours can be
applied to real-world problems.
Deoxyribonucleic acid, abbreviated and
commonly known as DNA, is a storage medium for genetic information and is
found
Euler Tour
Seven Bridges Problem
In this chapter we consider the following problem:
Suppose you are
going to a newly built shopping mall. You want to visit the whole shopping
mall, and you probably do not want to have any repetition, i.e., not to revisit