PPT-On the degree distribution of random planar graphs

Angelika Steger j oint work with Konstantinos Panagiotou SODA11 TexPoint fonts used in EMF Read the TexPoint manual before you delete this box A A A A A Random Graphs . Each edge is chosen independently with probability propor tional to the product of the expected degrees of its endpoints We examine the distribution of the sizesvolumes of the connected components which turns out depending primarily on the average d Scintigaraphy. Hui. Pan. Chapter 8, Planar . Scintigraphy. What is Planar . Scintigraphy. ?. Planar . Scintigraphy. : unlike x-ray imaging, use Anger scintillation camera, a type of electronic detection instrumentation, to generate . Anthony Bonato. Ryerson University. CanaDAM. 2011. Cop number of a graph. the . cop number of a graph. , written . c(G). , is an elusive graph parameter. few connections to other graph parameters. hard to compute. Carla . Binucci. , Emilio Di Giacomo, . Walter Didimo, Fabrizio Montecchiani, Maurizio . Patrignani. , . Ioannis. G. . Tollis. Fan-planar drawings. Fan-planar drawings. Given a graph G, a . fan-planar drawing . Laurent . Massouli. é & . Fabien Mathieu. laurent.massoulie@inria.fr. & . fabien.mathieu@inria.fr. . The . “Code Red. ” Internet Worm. Epid. e. mics. . & rumours. Propagate fast. Advanced Kernelization Techniques. Bart . M. P. . Jansen. Insert. «. Academic. unit» . on every page:. 1 Go to the menu «Insert». 2 Choose: Date and time. 3 Write the name of your faculty or department in the field «Footer». Drawing . a Graph with a . Planar . Subgraph. Marcus Schaefer. DePaul University. GD’14 . Würzburg. Speaker: Carsten . Gutwenger. Partial Planarity. “If you're given a graph in which some edges are allowed to participate in crossings while others must remain uncrossed, how can you draw it, respecting these constraints?”. . Intro problem- 3 houses and 3 utilities.  K. 3,3. problem: Can 3 houses be connected to 3 utilities so that no 2 lines cross?. Similarly, can an isomorphic version of K. 3,3. be drawn in the plane so that no two edges cross?. on Cops and Robbers. Anthony Bonato. Ryerson University. Genus. (Aigner, . Fromme. , 84) . planar graphs (genus . 0. ) have cop number . ≤ 3.. (Clarke, 02) . outerplanar. graphs have cop number . Eyal. Ackerman. University of Haifa and . Oranim. College. Drawing graphs in the plane. Consider drawings of graphs in the plane . s.t. .. No loops or parallel edges. Vertices .  distinct points. Anthony Bonato. Ryerson University. GRASCan’17. Grenfell Campus. Graphs on surfaces. ?. ?. S. 0. S. 1. Genus of a graph. a graph that can be embedded in an (orientable!) surface with . g. holes (and . Random Graphs. Random graphs. Erdös-Renyi. model . One of several models …. Presents a theory of how social webs are formed.. Start with a set of isolated nodes. Connect each pair of nodes with a probability. Erdős-Rényi. Random model, . Watts-. Strogatz. Small-world, . Barabási. -Albert Preferential attachment, . Molloy-Reed . Configuration model . and . Gilbert . Random . G. eometric model. Excellence Through Knowledge. Anthony Bonato. Ryerson University. CRM-ISM Colloquium. Université. Laval. Complex networks in the era of . Big Data. web graph, social networks, biological networks, internet networks. , …. Infinite random geometric graphs - Anthony Bonato.