Dependency tree

An arrow runs from a page to a page that rests on it: page B points at page A when some result on A depends, through the item graph, on a result whose home is B. Only pages in Combinatorics are shown; anything this group rests on from elsewhere in the library is listed below.

Pages, prerequisites first

• Finite Counting, Factorials and Binomial CoefficientsExamples & counterexamples →
• Inclusion–Exclusion, the Pigeonhole Principle and Double CountingExamples & counterexamples →
• Chains, Antichains, Sperner and DilworthExamples & counterexamples →
• Graphs, Walks and ConnectivityExamples & counterexamples →
• Eulerian and Hamiltonian GraphsExamples & counterexamples →
• Graph ColouringExamples & counterexamples →
• Incidence Algebras and Möbius InversionExamples & counterexamples →
• Induced Subgraphs and Hereditary Graph ClassesExamples & counterexamples →
• Ramsey TheoryExamples & counterexamples →
• Trees, Forests and Spanning TreesExamples & counterexamples →
• Matchings, Covers, Menger and Network FlowsExamples & counterexamples →
• Plane Graphs, Euler's Formula and the Five Colour TheoremExamples & counterexamples →

Rests on other groups

• Chains, Antichains, Sperner and Dilworth rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Chains, Antichains, Sperner and Dilworth — Examples rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Eulerian and Hamiltonian Graphs rests on Construction of the Natural Numbers, Countability and Uncountability, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Eulerian and Hamiltonian Graphs: Examples and Counterexamples rests on Construction of the Natural Numbers, Countability and Uncountability, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Finite Counting, Factorials and Binomial Coefficients rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Finite Counting, Factorials and Binomial Coefficients: Examples and Counterexamples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Graph Colouring rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Graph Colouring — Examples rests on Construction of the Natural Numbers, Countability and Uncountability, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Graphs, Walks and Connectivity rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Graphs, Walks and Connectivity — Examples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Incidence Algebras and Möbius Inversion rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Incidence Algebras and Möbius Inversion — Examples rests on Binary Operations, Monoids, Groups and Subgroups, Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Inclusion–Exclusion, the Pigeonhole Principle and Double Counting rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Inclusion–Exclusion, the Pigeonhole Principle and Double Counting: Examples and Counterexamples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Induced Subgraphs and Hereditary Graph Classes rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Induced Subgraphs and Hereditary Graph Classes — Examples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Matchings, Covers, Menger and Network Flows rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Matchings, Covers, Menger and Network Flows — Examples rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Plane Graphs, Euler's Formula and the Five Colour Theorem rests on Binary Operations, Monoids, Groups and Subgroups, Compactness in Metric Spaces, Completeness, Completion, and Uniform Continuity, Connectedness, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Continuity, IVT, EVT, and Uniform Continuity, Countability and Uncountability, Filters and Ultrafilters, Foundations of the Real Numbers for Analysis, Limits of Real Functions, Linear Independence, Bases and Dimension, Linear Transformations, Rank-Nullity and Quotient Spaces, Metric Spaces, Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness, Order, Zorn's Lemma, and the Axiom of Choice, Rⁿ as a Normed Space; Vector-Valued Functions, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, Sequences and Limits, Subspaces, Products, and Quotients, Suprema and Infima, The Topology of Euclidean Space, The ZFC Axioms and the Basic Set Constructions, Topological Spaces and Continuity, Topology of ℝ, Vector Spaces, Linear Subspaces, Span and Direct Sums
• Plane Graphs, Euler's Formula and the Five Colour Theorem — Examples rests on Binary Operations, Monoids, Groups and Subgroups, Compactness in Metric Spaces, Completeness, Completion, and Uniform Continuity, Connectedness, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Continuity, IVT, EVT, and Uniform Continuity, Countability and Uncountability, Filters and Ultrafilters, Foundations of the Real Numbers for Analysis, Limits of Real Functions, Linear Independence, Bases and Dimension, Linear Transformations, Rank-Nullity and Quotient Spaces, Metric Spaces, Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness, Order, Zorn's Lemma, and the Axiom of Choice, Rⁿ as a Normed Space; Vector-Valued Functions, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, Sequences and Limits, Subspaces, Products, and Quotients, Suprema and Infima, The Topology of Euclidean Space, The ZFC Axioms and the Basic Set Constructions, Topological Spaces and Continuity, Topology of ℝ, Vector Spaces, Linear Subspaces, Span and Direct Sums
• Ramsey Theory rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Limits of Real Functions, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, Suprema and Infima, The ZFC Axioms and the Basic Set Constructions
• Ramsey Theory — Examples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, Sequences and Limits, The ZFC Axioms and the Basic Set Constructions
• Trees, Forests and Spanning Trees rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, Suprema and Infima, The ZFC Axioms and the Basic Set Constructions
• Trees, Forests and Spanning Trees — Examples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, Suprema and Infima, The ZFC Axioms and the Basic Set Constructions