PPT-Fan-planar Graphs: Combinatorial Properties and Complexity

Carla Binucci Emilio Di Giacomo Walter Didimo Fabrizio Montecchiani Maurizio Patrignani Ioannis G Tollis Fanplanar drawings Fanplanar drawings Given a graph G a fanplanar drawing . Dwyane George. March 10, 2015. Outline. Definitions. Algorithm: Single-Source Shortest Path (SSSP. ). r. -Division (Clustering). Runtime Analysis. Proof . of . Correctness. Planar Graphs. Definition: a graph G that can be embedded in a plane, such that the edges only intersect at the endpoints. Angelika Steger. (j. oint. . work. . with. . Konstantinos . Panagiotou. , SODA‘11. ) . . TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. Random Graphs . Lecture 20: Nov 25. This Lecture. Graph coloring is another important problem in graph theory.. It also has many applications, including the famous 4-color problem.. Graph coloring. Applications. Planar graphs. Minors, . Bidimensionality. ,. & Decomposition. r. r. Erik Demaine. MIT. Goals. How far . beyond planar graphs . can we go?. Graphs excluding. a fixed minor. Powers thereof. Build . general approximation frameworks . . 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. Daniel Lokshtanov. Based on joint work with Hans Bodlaender ,Fedor Fomin,Eelko Penninkx, Venkatesh Raman, Saket Saurabh and Dimitrios Thilikos. Background. Most interesting graph problems are . NP-hard. 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 . Planar graphs. 2. Planar graphs. Can be drawn on the plane without crossings. Plane graph: planar graph, given together with an embedding in the plane. Many applications…. Questions:. Testing if a graph is planar. . and the . Power of Monotone Proofs. Sam Buss (UCSD), Valentine . Kabanets. (SFU), . Antonina . Kolokolova. (MUN), . Michal . Koucký. . (Charles U.). VNC. 1. TexPoint fonts used in EMF. . Announcements. A5 Heaps Due October 27. Prelim 2 in ~3 weeks: Thursday Nov 15. A4 being graded right now. Mid-Semester College Transitions Survey on Piazza. 2. These aren't the graphs we're looking for. What is the best way to measure the time complexity of an algorithm?. - Best-case run time?. - Worst-case run time?. - Average run time?. Which should we try to optimize?. Best-Case Measures. How can we modify almost any algorithm to have a good best-case running time?. Announcements. A5 Heaps Due October 27. Prelim 2 in ~3 weeks: Thursday Nov 15. A4 being graded right now. Mid-Semester College Transitions Survey on Piazza. 2. These aren't the graphs we're looking for.