阿摩線上測驗
登入
首頁
>
台大◆電機◆離散數學(B)
>
109年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所丙組:離散數學(B)#105860
> 申論題
5.(10 points) Let G = (V, E) be a simple planar undirected graph with every vertex ha 5. Is it true that G must have at least 12 vertices? Prove your answer.
相關申論題
1. (15 points) Let S be a set of n elements. Let A, B be two different subsets of S chosen uniformly al Tandom. What is the probability that A is a subset of B? Show your derivation.
#451281
2. (10 points) Solve the following recurrence (show your derivation):
#451282
3. (15 points) Find a positive integer p such that or show that such an integer does not exist. Prove the correctness of your answer. (a)
#451283
(b) In propositional logic, is a functionally complete set.
#451284
(c) If A and B are two countably infinite sets, then |A| = |B|.
#451285
(d) If S is an infinite set, then 2S must be uncountable.
#451286
(e) If a relation R is transitive, then R2 must also be transitive.
#451287
(f) The set is a partial ordering on the set of all positive functions f: N→ R+.
#451288
(g) If R1and R2 are two different relations defined on set A, then the (directed) graphs repre- senting R1 and R2 must not be isomorhpic.
#451289
6. (15 points) If a graph G has chromatic number k, but every graph G' resulting from removing one cdge from G has chromatic number at most k–1. Is it always true that every vertex in G has degree at least k–1? Prove your answer. Recall that the chromatic number of a graph is the minimum number of colors required to color all vertices such that adjacent vertices have different colors.
#451291
相關試卷
112年 - 112 國立臺灣大學_碩士班招生考試:數學(B)#130247
112年 · #130247
110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:離散數學(B)#101167
110年 · #101167
109年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所丙組:離散數學(B)#105860
109年 · #105860
阿摩線上測驗
登入