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Pearls in Graph Theory: A Comprehensive Introduction
Nora Hartsfield,Gerhard Ringel
No preview available - 2003
a a b antichains arbitrary bijection binary binomial bipartite graph Boolean algebras called cardinality circuit closure cocircuit coefficients colored columns combinatorial complement connected Consider contains coordinatization copoints Corollary corresponding cycle decomposition define Definition denote directed graph disjoint distributive lattice dual edges equivalent Example exists Figure finite lattice finite matroid finite set formula gammoid geometric lattice Hence implies incidence algebra independent sets induced integers inversion isomorphic K-linear Lemma Let G(V Let M(S linear locally finite poset Map(N mapping Math matrix matroid M(S minimal Mobius function modular lattices monotone n-set obtain operator partial transversal permutation group planar planar graph points polygon matroid polynomial precisely Proof Proposition Prove rank function recursion result satisfies semimodular sequence set system Show subgraph sublattice subsets subspace Suppose symmetric theorem theory transversal matroid trivial unique vector space Verify vertex vertex-set vertices whence