Elements of Discrete Mathematics in Problems

[299/67%]

A. A. Glibichuk, A. B. Daynyak, D. G. Ilyinsky, A. B. Kupavskii, A. M. Raigorodskii, A. B. Skopenkov, A. A. Chernov

Chapter 1Elements of Combinatorics[66/76%]

Section 1.1Counting and Combinatorial Identities[6/83%]

Section 1.2The Inclusion-Exclusion Formula[6/67%]

Section 1.3The Pigeonhole Principle[9/89%]

Section 1.4Combinatorics of the Boolean Cube[7/57%]

Section 1.5Möbius Inversion[6/100%]

Section 1.6Double Counting[8/100%]

Section 1.7Permutations[9/78%]

Section 1.8Parity of Permutations[6/67%]

Section 1.9Combinatorics of Equivalence Classes[9/44%]

Chapter 2Fundamentals of Graph Theory[52/56%]

Section 2.1Basic Definitions[4/25%]

Section 2.2Enumeration of Trees[6/50%]

Section 2.3Graphs up to Isomorphism[5/20%]

Section 2.4Planar Graphs[9/44%]

Section 2.5Eulerian Paths and Cycles[8/50%]

Section 2.6Hamiltonian Paths and Cycles[8/88%]

Section 2.7Extremal Problems (Turán's Theorem)[6/83%]

Section 2.8Menger's Theorem[6/67%]

Chapter 3Graph Colorings and Polynomials[23/57%]

Section 3.1Graph Colorings[11/55%]

Section 3.2Chromatic Number and Index[4/100%]

Section 3.3The Chromatic Polynomial and the Tutte Polynomial[8/38%]

Chapter 4Fundamentals of Ramsey Theory[29/90%]

Section 4.1Two-Color Ramsey Numbers[7/100%]

Section 4.2Multicolor Ramsey Numbers[7/86%]

Section 4.3Ramsey Numbers for Hypergraphs[4/100%]

Section 4.4Ramsey-Type Results[6/83%]

Section 4.5Ramsey Numbers for Subgraphs[5/80%]

Chapter 5Set Systems (Hypergraphs)[37/70%]

Section 5.1Intersections of Subsets[5/80%]

Section 5.2Systems of Common Representatives[6/67%]

Section 5.3Systems of Distinct Representatives[8/63%]

Section 5.4The Permanent[4/25%]

Section 5.5Vapnik-Chervonenkis Dimension[9/89%]

Section 5.6Sunflowers[5/80%]

Chapter 6Analytic and Probabilistic Methods[53/62%]

Section 6.1Asymptotics[12/75%]

Section 6.2Independence and Existence Proofs[26/58%]

Section 6.3Random Graphs[15/60%]

Chapter 7Algebraic Methods[20/45%]

Section 7.1The Linear-Algebraic Method in Combinatorics[9/78%]

Section 7.2Hadamard Matrices[11/18%]

Chapter 8Incidence Theorems in Geometry[7/100%]

Section 8.1Problems[7/100%]

Chapter 9Additive Combinatorics[12/50%]

Section 9.1Problems[12/50%]