Excluding a long double path minor
The "height" of a graph G is defined to be the number of steps to construct G by two simple graph operations. Let Bn be the graph obtained from an n-edge path by doubling each edge in parallel. Then, for any minor-closed class script G of graphs, the following are proved to be equivalent: (1) Some Bn is not in script G; (2) There is a number h such that every graph in script G has height at most h; (3) script G is well-quasi-ordered by the topological minor relation; (4) There is a polynomial function p( • ) such that the number of paths of every graph G in script G is at most p(\V(G)\ + \E(G)\). © 1996 Academic Press, Inc.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Ding, G. (1996). Excluding a long double path minor. Journal of Combinatorial Theory. Series B, 66 (1), 11-23. https://doi.org/10.1006/jctb.1996.0002