The complexity of some graph problems with bounded minors of their constraint matrices

The article considers natural formulations of the independent set problem, vertex and edge dominating set problems as integer linear programming problems. For every fixed $C$, authors prove polynomial-time solvability of both dominating set problems in a class of graphs, for which all minors of the vertex and edge adjacency matrices are at most $C$ in the absolute value. The paper also includes a similar result for the independent set problem and for a class of graphs, which is defined by bounding of absolute values of all matrix minors obtained by augmenting of transposed incidence matrices by all-ones vectors.