1990/01/01 by Noga Alon, Paul Seymour, Robin Thomas · 2 citations
Computer Science · Mathematics · Engineering · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Optimization and Search Problems #Tel aviv #IBM #Citation #Atlanta #Library science #Genizah #Research center #Minor (academic) #Computer science #Mathematics #Operations research #Engineering #History #Physics #Archaeology #Art #Political science #Metropolitan area #Humanities
paper · pdf · doi:10.1145/100216.100254
openalex publication_date 1990/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
corresponds to G in time 0(n3/2). We also describe Let G be an n-vertex graph with nonnegative weights whose sum is 1 assigned to its vertices, and with no minor isomorphic to a given h-vertex graph H. We prove that there is a set X of no more than h3/2nl/2 vertices of G whose deletion creates a graph in which the total weight of every connected component is at most 1/2. This extends significantly a well-known theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds, given an n-vertex graph G with weights as above and an h-vertex graph H, either such a set X or a minor of G isomorphic to H. The algorithm runs in time O(hl/2nl/2m), where m is the number of edges of G plus the number of its vertices. Our results supply extensions of the many known applications of the Lipton-Tarjan separator theorem from the class of planar graphs (or that of graphs with bounded genus) to any class of graphs with an excluded minor. For example, it follows that for any fixed graph H, given a graph G with n vertices and with no H-minor one can approximate the size of the maximum independent set of G up to a relative error of 1/~/l-b-~ in polynomial time, find that size exactly and find the chromatic number of G in time 2 ('~-) and solve any sparse system of n linear equations in n unknowns whose sparsity structure