MY-ASSIGNMENTEXPERT™可以为您提供 sydney MATH2069 Graph Theory图论的代写代考和辅导服务！
这是悉尼大学图论课程的代写成功案例。
MATH2069课程简介
This unit introduces students to several related areas of discrete mathematics, which serve their interests for further study in pure and applied mathematics, computer science and engineering. Topics to be covered in the first part of the unit include recursion and induction, generating functions and recurrences, combinatorics. Topics covered in the second part of the unit include Eulerian and Hamiltonian graphs, the theory of trees (used in the study of data structures), planar graphs, the study of chromatic polynomials (important in scheduling problems).
Prerequisites
At the completion of this unit, you should be able to:
- LO1. identify and use combinatorial objects involved in counting problems to solve them
- LO2. solve linear recurrence relations by using generating functions and characteristic equations
- LO3. identify Eulerian and Hamiltonian graphs
- LO4. apply special algorithms to find minimal walks in weighted graphs
- LO5. apply special algorithms to find spanning trees in graphs
- LO6. find chromatic numbers and chromatic polynomials of graphs.
MATH2069 Graph Theory HELP（EXAM HELP， ONLINE TUTOR）
Given a set of lines in the plane with no three meeting at a common point, form a graph $G$ whose vertices are the intersections of the lines with two vertices adjacent if they appear consecutive on one of the lines. Prove that $\chi(G) \leq 3$.
Let $G$ be a graph such that every pair of odd cycles in $G$ have a common vertex. Prove that $\chi(G) \leq 5$.
Without using the weak (nor the strong) perfect graph theorem, prove that the complement of a bipartite graph is perfect.
Prove that Brooks’ Theorem is equivalent to the following statement: Every $k-1$ regular $k$-critical graph is a clique or an odd cycle.
Prove that for every graph $G, \chi(G)+\chi(\bar{G}) \leq n(G)+1$.
The Knesser graph $K G_{n, k}$ (for $1 \leq k \leq \frac{n}{2}$ ) is the graph whose vertices are all $k$ subsets (i.e., subsets of cardinality $k$ ) of an $n$ element set and whose edges are all pairs of vertices that correspond to disjoint sets. Prove that $\chi\left(K G_{n, k}\right) \leq n-2 k+2$.
Prove that the vertices of every connected graph on at least 8 vertices with maximum degree 6 can be colored with 3 colors so that no odd cycle is monochromatic.
MY-ASSIGNMENTEXPERT™可以为您提供 SYDNEY MATH2069 GRAPH THEORY图论的代写代考和辅导服务！
