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Mathematics for Computer Science - MIT OpenCourseWare

Mcs 2015/5/18 1:43 page i #1 Mathematics for Computer Science revised Monday 18th May, 2015, 01:43 Eric Lehman Google Inc. F Thomson LeightonDepartment of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies Albert R MeyerDepartment of Electrical Engineering and Computer Science and the Computer Science and AI Laboratory, Massachussetts Institute of Technology 2015, Eric Lehman, F Tom Leighton,Albert R Meyer. This work is available under the terms of theCreative CommonsAttribution-NonCommercial-ShareAl ike license. mcs 2015/5/18 1:43 page ii #2 mcs 2015/5/18 1:43 page iii #3 Contents I Proofs Introduction 3 References 4 1 What is a Proof?

11.4 Isomorphism 399 11.5 Bipartite Graphs & Matchings 401 11.6 The Stable Marriage Problem 406 11.7 Coloring 413 11.8 Simple Walks 417 11.9 Connectivity 419 11.10 Forests & Trees 424 11.11 References 433 12 Planar Graphs 473 12.1 Drawing Graphs in the Plane 473 12.2 Definitions of Planar Graphs 473 12.3 Euler’s Formula 484

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