Combinatorial problems and exercises
Basic enumeration; The sieve; Permutations; Two classical enumeration problems in graph theory; Connectivity; Factors of graphs; Extremal problems for graphs; Spectra of graphs; Automorphism of graphs; Hypergraphs; Ramsey theory.
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Hypergraphs circuits transversal theory intersection
moment method Moebius function 19 97
Permutations cycle index polynomial HallRenyi
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2-coloration 2-connected a-critical adjacent assume automorphism group bipartite graph classes complete graph components of G connected graph Consider contradiction cycle cycle index defined degree at least denote the number digraph disjoint edges of G eigenvalues eigenvector elements endpoints Euler trail exactly follows formula graph G Hamiltonian circuit Hamiltonian path Hence hint hypergraph independent set induced subgraph induction hypothesis inner points integers isomorphic joined length Let G Math matrix maximum independent set maximum matching Menger's theorem minimal neighbors number of edges number of partitions number of points obviously odd circuit orientation path permutation planar planar graph points of degree points of G polynomial proves the assertion r-regular recurrence relation remove resulting graph satisfies sequence Similarly simple graph solution spanning tree strongly connected subset Suppose indirectly theorem triangle trivial whence xv x2