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Tiled partial cubes

✍ Scribed by Boštjan Brešar; Wilfried Imrich; Sandi Klavžar; Henry Martyn Mulder; Riste Škrekovski

Book ID
102341532
Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
130 KB
Volume
40
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

In the quest to better understand the connection between median graphs, triangle‐free graphs and partial cubes, a hierarchy of subclasses of partial cubes has been introduced. In this article, we study the role of tiled partial cubes in this scheme. For instance, we prove that almost‐median graphs are tiled and that tiled partial cubes are semi‐median. We also describe median graphs as tiled partial cubes without convex Q and extend an inequality for median graphs to a larger subclass of partial cubes. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 91–103, 2002

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