'Planar graph' diaporamas de présentation

Hamilton Graph Theory ??? 1. ?????????? ??????????? ?.6/7 ?????? 14 2. ???????????? ????????? ?.6/7 ?????? 20 3. ???????

Hamilton Graph Theory ??? 1. ?????????? ??????????? ?.6/7 ?????? 14 2. ???????????? ????????? ?.6/7 ?????? 20 3. ?????????? ???????????? ?.6/7 ?????? 22. ????????????.

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The Infamous Five Color Theorem

The Infamous Five Color Theorem. Dan Teague NC School of Science and Mathematics teague@ncssm.edu. 5-coloring of the continental US. 5 - c o l o r vertex coloring of the continental US. Augustus de Morgan, Oct. 23, 1852. In a letter to Sir William Hamilton,

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On Delivery Guarantees of Face and Combined Greedy-Face Routing in Ad Hoc and Sensor Networks

On Delivery Guarantees of Face and Combined Greedy-Face Routing in Ad Hoc and Sensor Networks. Hannes Frey, Ivan Stojmenovic MobiCom 2006. Face Recovery Details. When to change current face traversal? How to decide the next face locally?. Example 1.

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NP-Completeness

NP-Completeness. Observation. All problems below are NP-complete and polynomial reduce to one another!. by definition of NP-completeness. CIRCUIT-SAT. 3-SAT. 3-SAT reduces to INDEPENDENT SET. INDEPENDENT SET. DIR-HAM-CYCLE. GRAPH 3-COLOR. SUBSET-SUM. VERTEX COVER. SCHEDULING.

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Bounds on the Geometric Mean of Arc Lengths for Bounded-Degree Planar Graphs

Bounds on the Geometric Mean of Arc Lengths for Bounded-Degree Planar Graphs. M. K. Hasan Sung-eui Yoon Kyung-Yong Chwa KAIST, Republic of Korea. Image Rendering. Image Rendering. Image Rendering. Image Rendering. Image Rendering. Two Level I/O Memory Model. 2-block cache. a. c. e.

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Acyclic Colorings of Graph Subdivisions

Acyclic Colorings of Graph Subdivisions. 1 Debajyoti Mondal 2 Rahnuma Islam Nishat 2 Sue Whitesides 3 Md . Saidur Rahman. 1 University of Manitoba, Canada 2 University of Victoria, Canada 3 Bangladesh University of Engineering and Technology (BUET), Bangladesh. Acyclic Coloring. 6.

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Discrete and Combinatorial Mathematics R. P. Grimaldi , 5 th edition, 2004

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Part 10. Graphs

Part 10. Graphs. CS 200 Algorithms and Data Structures. Outline. Introduction Terminology Implementing Graphs Graph Traversals Topological Sorting Shortest Paths Spanning Trees Minimum Spanning Trees Circuits. Circuits. Cycle

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Graph Theory

Graph Theory. CSRU1400, Fall 2007 Ellen Zhang. Outline. Introduction to graph Is there a Eulerian trail, curcuit? Isomorphism and planarity Shortest path problem. Graph. G=(V,E), V is the set of vertices (nodes), E is the set of edges

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Computational Geometry

Computational Geometry. Piyush Kumar (Lecture 10: Point Location). Welcome to CIS5930. Planar Point Location. Given a polygonal subdivision of the plane (a PSLG) , Preprocess to answer which face a query point lies in. Assume Input has n vertices. Step 1. Triangulate. Step 2.

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Chapter 10.7 Planar Graphs

Chapter 10.7 Planar Graphs

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Final Review

Final Review. Chris and Virginia. Overview. One big multi-part question. (Likely to be on data structures) Many small questions. (Similar to those in midterm 2) A few questions from the homework and class. (This slide is on the class webpage). You need to able to.

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Biased Positional Games and the Erd ? s Paradigm

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11. ??????????

11. ??????????. ??. ????? ????? ??? ????????? etc. ?????????????????. ??? ??. ?????. ????? (maximum flow problem) ???????????? (network flow problem) ???????????? ?????????????????. 5/5. 4/4. 6/8. 9. 1/2. 9. 0/3. 1/1. 5/5. 3/3. 4/4. ????? ????????????? ??????????

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Sec. 5.1: Planarity & Coloring

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Primal-dual algorithms for node-weighted network design in planar graphs

Primal-dual algorithms for node-weighted network design in planar graphs. Grigory Yaroslavtsev Penn State (joint work with Piotr Berman). Feedback Vertex Set Problems. Given: a collection of cycles in a graph Goal: break them, removing a small # of vertices.

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Graph Vertex Colorability & the Hardness

Dec. 15 th , Presentation for Final Project. Graph Vertex Colorability & the Hardness. Mengfei Cao COMP-150 Graph Theory Tufts University . Framework. In General: Graph-2-colorability is in N Graph-3-colorability is NP-complete (Reduce to k?4 ) [2]

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Undirected graphs

Undirected graphs.

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MATH 370 Final Review

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