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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A separator theorem for nonplanar graphs
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by Noga Alon, Paul Seymour and Robin Thomas PDF
J. Amer. Math. Soc. 3 (1990), 801-808 Request permission

Abstract:

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 ${h^{3/2}}{n^{1/2}}$ 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 $O({h^{1/2}}{n^{1/2}}m)$, where $m = \left | {V(G)} \right | + \left | {E(G)} \right |$.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 3 (1990), 801-808
  • MSC: Primary 05C40; Secondary 05C85, 68Q25, 68R10
  • DOI: https://doi.org/10.1090/S0894-0347-1990-1065053-0
  • MathSciNet review: 1065053