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21 May 2005: The Erdős-Stone Theorem, probabilistic methods, and eigenvalue methods, are new to thepresent Graph Theory course.

14 Oct 2005: The Erdős-Stone Theorem, probabilistic methods, and eigenvalue methods, are new to thepresent Graph Theory course.

21 May 2005: MATHEMATICAL TRIPOS PART II (2004–05). Coding and Cryptography - Sample Tripos Questions T.A. Fisher. Note: This course is an extension of the Part IIA Coding and Cryptography course. So there are. plenty of past tripos questions available. (See

10 Nov 2005: un} and satisfyingχ(Gk) = k. Construct a graph Gk1 from Gk by adding new vertices {w,v1,. ... 22) Let G be the graph of order 2n1 obtained by subdividing a single edge of Kn,n bya new vertex.

21 May 2005: un} and satisfyingχ(Gk) = k. Construct a graph Gk1 from Gk by adding new vertices {w,v1,. ... Construct explicitly such graphs for k 4. 37) Let G be the graph of order 2n1 obtained by subdividing a single edge of Kn,n bya new vertex.

24 Nov 2005: I therefore find a new pair of primes andannounce that I shall be using the Rabin Williams scheme with modulus N′ > N. ... 58) Suppose we drop the requirement 1 r p 1 from the el Gamal signature scheme.How might we then be able to forge new signatures

21 May 2005: I therefore find a new pair of primes andannounce that I shall be using the Rabin Williams scheme with modulus N′ > N. ... 74) Suppose we drop the requirement 1 r p 1 from the el Gamal signature scheme.How might we then be able to forge new signatures

21 May 2005: Compute the capacity ofthe new channel. 33) Consider two DMC’s of capacity C1 and C2 with each having input alphabet Σ1 andoutput alphabet Σ2.

21 May 2005: b) Prove Euler’s theorem: If P is a convex polyhedron in R3, then F EV = 2.[Hint: Put a new vertex at the center of each polygonal face.].

21 May 2005: Please send comments and corrections(especially important for the new questions) to m.hyland@dpmms.cam.ac.uk.

21 May 2005: so add thatmultiple of dc0,1,10 to get a new cycle (representing the same element ofhomology) with the coefficient of c0,10 also zero.