1 / 32

Some NP-complete Problems in Graph Theory

Lecture 31. Some NP-complete Problems in Graph Theory. Prof. Sin-Min Lee. Graph Theory. An independent set is a subset S of the verticies of the graph, with no elements of S connected by an arc of the graph. Coloring.

awena
Télécharger la présentation

Some NP-complete Problems in Graph Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 31 Some NP-complete Problems in Graph Theory Prof. Sin-Min Lee

  2. Graph Theory

  3. An independent set is a subset S of the verticies of the graph, with no elements of S connected by an arc of the graph.

  4. Coloring • How do you assign a color to each vertex so that adjacent vertices are colored differently? • Chromatic number of certain types of graphs. • k-Coloring is NP Complete. • Edge coloring

  5. Planarity and Embeddings K4 is planar K5 is not Euler’s formula Kuratowski’s theorem Planarity algorithms

  6. BB: III – maybe two weeks? AG: CH. 4 and 5. Flows and Matchings 3 6 • Meneger’s theorem (separating vertices) • Hall’s theorem (when is there a matching?) • Stable matchings • Various extensions and similar problems • Algorithms 7 t 5 2 1 1 4 s 5 3 9 girls boys

  7. Random Graphs • Form probability spaces containing graphs or sequences of graphs as points. • Simple properties of almost all graphs. • Phase transition: as you add edges component size jumps from log(n) to cn.

  8. Algebraic Graph Theory a a3 a2 group elements a a • Cayley diagrams • Adjacency and Laplacian Matrices their eigenvalues and the structure of various classes of graphs a 1 a generators

  9. Algorithms • DFS, BFS, Dijkstra’s Algorithm... • Maximal Spanning Tree... • Planarity testing, drawing... • Max flow... • Finding matchings... • Finding paths and circuits... • Traveling salesperson algorithms... • Coloring algorithms...

More Related