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Main Title: Edge-Dominating Trails in AT-free Graphs
Author(s): Köhler, Ekkehard
Kriesell, Matthias
Type: Research Paper
Abstract: A triple of independent vertices of a graph G is called an asteroidal triple} (AT) if between any two of them there exists a path in G that does not intersect the neighborhood of the third. In this paper we consider different classes of graphs that are related to AT-free graphs. We start by examining AT-free line graphs, give a characterization of them, and apply this for showing that all connected AT-free line graphs are traceable. In the second part we consider line graphs of AT-free graphs. Here we prove that every AT-free graph contains an edge-dominating trail, and that, consequently, every line graph of an AT-free graph is traceable. Moreover, we give an algorithm to find such an edge-dominating trail. In the third part of the paper we consider claw-free AT-free graphs and show a couple of Hamiltonian properties for them, using the RYJÁČEK closure. In the last section we give a characterization of all AT-free graphs with maximum degree at most 3.
Subject(s): trails
asteroidal triple
AT-free graphs
Issue Date: 1998
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1998, 615
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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