TY - JOUR
T1 - A separator theorem for nonplanar graphs
AU - Alon, Noga
AU - Seymour, Paul
AU - Thomas, Robin
PY - 1990/10
Y1 - 1990/10
N2 - Let G be an n-vertex graph with no minor isomorphic to an h-vertex complete graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than (Eqution presented) vertices. This extends a theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds such a partition (A, B, C) in time O(h½ n½m) where m = V(G) + E(G).
AB - Let G be an n-vertex graph with no minor isomorphic to an h-vertex complete graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than (Eqution presented) vertices. This extends a theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds such a partition (A, B, C) in time O(h½ n½m) where m = V(G) + E(G).
UR - http://www.scopus.com/inward/record.url?scp=84968494230&partnerID=8YFLogxK
U2 - 10.1090/S0894-0347-1990-1065053-0
DO - 10.1090/S0894-0347-1990-1065053-0
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AN - SCOPUS:84968494230
SN - 0894-0347
VL - 3
SP - 801
EP - 808
JO - Journal of the American Mathematical Society
JF - Journal of the American Mathematical Society
IS - 4
ER -