For each infinite cardinal k we give several necessary and sufficient conditions for a graph not to contain a minor isomorphic to the infinite k-branching tree in terms of a certain kind of a “tree-decomposition,” in terms of a “path-decomposition,” and alsoin terms of a “cops-and-robber game.” We also give necessary and sufficient conditions for a graph not to contain a subgraph isomorphic to a subdivision of the same tree.
|Original language||English (US)|
|Number of pages||34|
|Journal||Transactions of the American Mathematical Society|
|State||Published - 1993|
All Science Journal Classification (ASJC) codes
- Applied Mathematics