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Main Title: Recognizing Graphs without Asteroidal Triples
Author(s): Köhler, Ekkehard
Type: Research Paper
Abstract: We consider the problem of recognizing AT-free graphs. Although there is a simple O(n3) algorithm, no faster method for solving this problem had been known. Here we give three different algorithms which have a better time complexity for graphs which are sparse or have a sparse complement; in particular we give algorithms which recognize AT-free graphs in O(n m} + n2), O( m}3/2 + n2), and O(n2.82 + n m). In addition we give a new characterization of graphs with bounded asteroidal number by the help of the knotting graph, a combinatorial structure which was introduced by Gallai for considering comparability graphs.
Subject(s): graph
asteroidal triple-free
Issue Date: 2000
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2000, 705
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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