% min_walk_reduced -- theorem that minimum walk is reduced % min_walks -- minimum walk satisfying a propertyx % path_ops -- deleting vertex and edge operations % paths -- fundamental definition and properties about paths % reduce_walks -- operation to reduce a walk % sep_sets -- definition of separating sets % di_subgraphs -- generation of di_subgraphs from vertex sets % di_subgraphs_from_walk -- generation of di_subgraphs from walks % subtrees -- subtrees of a digraph % trees -- fundamental definition of trees % walk_inductions -- induction on length of a walk % walks -- fundamental definition and properties of walks % %------------------------------------------------------------------------------
top: THEORY
% digraph_deg_sum -- theorem relating vertex degree and number of edges % tree_circ -- theorem that tree has no circuits % digraph_connected -- all connected defs are equivalent % ramsey_new -- Ramsey's theorem % menger -- menger's theorem % tree_paths -- theorem that tree has only one path between vertices % circuit_deg -- degree of circuits % cycle_deg -- theorem about degree and existence of cycle % digraph_complected -- unusual definition of connected digraph % digraph_conn_piece -- structural connected ==> piece connected % digraph_path_conn -- path connected ==> structural connected % digraph_piece_path -- piece connected ==> path connected % h_menger -- hard menger % meng_scaff -- scaffolding for hard menger proof % meng_scaff_defs -- scaffolding for hard menger proof % meng_scaff_prelude -- scaffolding for hard menger proof % sep_set_lems -- properties of separating sets
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