PPT-Graph Theory –

Proofs that K5 and K33 are not planar Copyright R F Barrow 2009 all rights reserved wwwwaldomathscom K 5 K 33 The Proofs that K 5 and K 33 are not planar Complete graph with 5 nodes. We call the tail of the head of and uv the ends of If there is an edge with tail and head then we let uv denote such an edge and we say that this edge is directed from to Loops Parallel Edges and Simple Digraphs An edge uv in a digraph is a Anand Tripathi, Vinit Padhye, . Tara Sasank Sunkara. Department of Computer Science. University of Minnesota. . Presentation by . Tara Sasank Sunkara. eBay Inc.. Acknowledgements:. This work was partly supported by NSF award 1319333. Simon Prince. s.prince@cs.ucl.ac.uk. Plan of Talk. Denoising. problem. Markov random fields (MRFs). Max-flow / min-cut. Binary MRFs (exact solution). Binary . Denoising. Before. After. Image represented as binary discrete variables. Some proportion of pixels randomly changed polarity.. Extremal graph theory. L. á. szl. ó. . Lov. á. sz. . Eötvös. . Lor. ánd. . University, Budapest . May 2012. 1. May 2012. 2. Recall some. . math. t. (. F. ,. G. ):. . Probability that random . Wei Wang. Department of Computer Science. Scalable Analytics Institute. UCLA. weiwang@cs.ucla.edu. Graphs/Networks. FFSM (ICDM03), SPIN (KDD04),. GDIndex. (ICDE07). MotifMining. (PSB04, RECOMB04, ProteinScience06, SSDBM07, BIBM08). L. á. szl. ó. . Lov. á. sz. . Eötvös. . Lor. ánd. . University, . Budapest. IAS, Princeton. . June 2011. 1. June 2011. Limit . theories. of . discrete. . structures. trees. graphs. digraphs. . social . and neural network data. Darren A. Narayan. Rochester Institute of Technology. Joint work with Roger Vargas, Williams College, Bradford Mahon and Frank Garcea, Rochester Center for Brain Imaging, University of Rochester. Hao Wei. 1. , . Jeffrey Xu Yu. 1. , Can L. u. 1. , . Xuemin. Lin. 2. . 1 . The . Chinese University of Hong Kong, Hong Kong. 2 . The . University of New South Wales. , . Sydney, Australia. Graph in Big Data . Thursday, March 27, 14. Bandwidth/. C. utwidth. When the vertices of a graph . G . are numbered with distinct integers, the . dilation . is the . maximum. difference between integers assigned to adjacent vertices. . ECE 580. 12. Graph Theory, Topological Analysis - Terms. Topological Analysis: General, systematic, suited for CAD. Graph. : Nodes and directed branches, describes the topology of the circuit, ref. direction. Helps visualize CAD. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. 1. Learning Objectives:. Know how to use graphs as models and how to determine efficient paths.. Modeling with graphs. Euler circuits. Degrees of vertices and Euler’s Theorem. Chapter . 7 Graph Theory. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Outline. Min s-t cut problem. Adjacency List. Adjacency-Matrix. Pointers/memory for each node (actually a form of adjacency list). Adjacency List. List of pointers for each vertex. Undirected Adjacency List. Adjacency List. The sum of the lengths of the adjacency lists is 2|E| in an undirected graph, and |E| in a directed graph..