**Proof - Euler Trail Theorem (1)**

An Euler trail is a walk that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph exactly once. A Euler trail with same endpoints is a Euler circuit. Here are some examples: Letbe a finite connected graph and denote the number of vertices that have odd degrees. Prove that G has a Euler trail if and only if . First, by the Handshake Theorem, we c..

**The Handshake Theorem and Its Corollary**

Prove that for , . Intuition: Suppose n people shake hands with other people in the group. They don't shake hands twice with the same person.How many handshakes take place?각 사람을 노드로 본다면 두 사람이 악수를 하면 그 두 노드 사이에 Edge 가 생긴다.전체 악수의 수 = Number of Edges in the graph = 각 사람이 한 악수의 수의 총합 / 2 = Sum of degree of every vertex / 2 Let be the vertices of G and their degrees respectively. Also, Then we know t..

**Loop Invariant Practice - Merge() of MergeSort()**

How to Think about Algorithms by Edmonds has good in-depth explanation of how to actually go about thinking about designing algorithms and approaching algorithmic problems. I applied the process to understanding Merge() routine of the MergeSort algorithm.

**공지사항**

**최근에 올라온 글**

**최근에 달린 댓글**

- Total
- 1,072

- Today
- 0

- Yesterday
- 0

**링크**

**TAG**

- #props
- Circuit
- cycle
- degree
- #uncontrolled_components
- Edmonds
- HTTAA
- relation
- #Mutual_Exclusivity
- #BMI
- image
- subgraph
- #Mutual_Exhaustivity
- codomain
- #Combinations
- #Constructive_Counting
- #onChange
- Induction
- Graph
- TIP
- trail
- #Counting
- definitions
- #Circular_Permutations
- #controlled_components
- proof
- Component
- #Permutations
- surjective
- #state