PPT-A counterexample for the graph area law conjecture

Dorit Aharonov Aram Harrow Zeph Landau Daniel Nagaj Mario Szegedy Umesh Vazirani arXiv14100951 Background local Hamiltonians H ij 1 Assume degree const. Proof of the middle levels conjecture. Hamilton . cycles. Hamilton . cycl. e = . cycle. . that. . visits. . every. . vertex. . exactly. . once. Hamilton . cycles. Problem:. . Given. a . graph. 2-1 Inductive Reasoning and Conjecture. Real - Life. Vocabulary. Inductive Reasoning. - reasoning that uses a number of specific examples to arrive at your conclusion. Conjecture- . a concluding statement reached using inductive reasoning. Patterns and Inductive Reasoning. Geometry 1.1. You may take notes on your own notebook or the syllabus and notes packet.. Make sure that you keep track of your vocabulary. One of the most challenging aspects of geometry compared to other math classes is the vocabulary!. Pearson . Pre-AP Unit 1. Topic . 2: Reasoning and Proof. 2-1. : . Patterns and Conjectures. Pearson Texas Geometry ©2016 . Holt Geometry Texas ©2007 . TEKS Focus:. (4)(C) Verify that a conjectures is false using a counterexample.. – Meyniel’s conjecture. Dr. Anthony Bonato. Ryerson University. AM8002. Fall . 2014. How big can the cop number be?. if G is disconnected of order n, then we can have c(G) = n (example?). c(n) = maximum cop number of a . polyhedra. ”. Instructor: Dr. Deza. Presenter: Erik Wang . Nov/2013. Agenda. Indentify the problem. The best upper bound. Summary. Identify the problem . Concepts - Diameter of graph. The “graph of a . Topics in Discrete Mathematics. Week 9 – Meyniel’s conjecture. Dr. Anthony Bonato. Ryerson University. Ryerson Mathematics . Winter . 2016. How big can the cop number be?. if G is disconnected of order n, then we can have c(G) = n (example?). Proof of the middle levels conjecture. Hamilton . cycles. Hamilton . cycl. e = . cycle. . that. . visits. . every. . vertex. . exactly. . once. Hamilton . cycles. Problem:. . Given. a . graph. Inductive Reasoning . When you use a pattern to find the next term in a sequence you’re using . inductive reasoning.. The conclusion you’ve made about the next terms in the pattern are called a . . with. Pascal Su (ETH . Zurich. ). Bipartite . Kneser. graphs are Hamiltonian. Hamilton . cycles. Hamilton . cycl. e = . cycle. . that. . visits. . every. . vertex. . exactly. . once. Hamilton . Chapter 2 . Student Notes. 2.1. Inductive Reasoning . and Conjecture. Conjecture -. Make a conjecture from the given statement.. Given: The toast is burnt.. Conjecture: ___________________________. To form conjectures through inductive reasoning. To disprove a conjecture with a counterexample. To avoid fallacies of inductive reasoning. Example 1. You’re at school eating lunch. You ingest some air while eating, which causes you to belch. Afterward, you notice a number of students staring at you with disgust. You burp again, and looks of distaste greet your natural bodily function. You have similar experiences over the course of the next couple of days. Finally, you conclude that belching in public is socially unacceptable. The process that lead you to this conclusion is called. To form conjectures through inductive reasoning. To disprove a conjecture with a counterexample. To avoid fallacies of inductive reasoning. Example 1. You’re at school eating lunch. You ingest some air while eating, which causes you to belch. Afterward, you notice a number of students staring at you with disgust. You burp again, and looks of distaste greet your natural bodily function. You have similar experiences over the course of the next couple of days. Finally, you conclude that belching in public is socially unacceptable. The process that lead you to this conclusion is called. Dorit. . Aharonov. Aram Harrow. Zeph. Landau. Daniel . Nagaj. Mario . Szegedy. Umesh. . Vazirani. arXiv:1410.0951. Background: local Hamiltonians. || . H. i,j. . || ≤ 1. Assume: . degree ≤ . const.