TITLE: Graph Minor check
QUESTION [6 upvotes]: Are there any good algebraic/algorithmic tools available to check if a given graph $H$ is a minor of $G$ from the adjacency matrix of $G$?

REPLY [5 votes]: A polynomial time algorithm for this is given in 
Robertson + Seymour, Graph minors. XIII. The disjoint paths problem, Journal of
Combinatorial Theory, Series B, 63 (1995), pp. 65–110.