{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture05 - CSE 421 Algorithms Richard Anderson Lecture 5...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
CSE 421 Algorithms Richard Anderson Lecture 5 Graph Theory
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Bipartite A graph is bipartite if its vertices can be partitioned into two sets V 1 and V 2 such that all edges go between V 1 and V 2 A graph is bipartite if it can be two colored
Image of page 2
Theorem: A graph is bipartite if and only if it has no odd cycles If a graph has an odd cycle it is not bipartite If a graph does not have an odd cycle, it is bipartite
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Lemma 1 If a graph contains an odd cycle, it is not bipartite
Image of page 4
Lemma 2 If a BFS tree has an intra-level edge , then the graph has an odd length cycle Intra-level edge: both end points are in the same level
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Lemma 3 If a graph has no odd length cycles, then it is bipartite No odd length cycles implies no intra-level edges No intra-level edges implies two colorability
Image of page 6
Connected Components Undirected Graphs
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Computing Connected Components in O(n+m) time A search algorithm from a vertex v can find all vertices in v’s component While there is an unvisited vertex v, search from v to find a new component
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern