8
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Skeletons, recognition algorithm and distance matrix of quasi-median graphs

Pages 155-171 | Received 15 Aug 1994, Published online: 20 Mar 2007
 

Abstract

A quasi-median graph can be characterized as a weak retract of a Cartesian product of complete graphs or equivalently as a graph of finite windex. We derive a new characterization of quasi-median graphs which allows us to recognize these graphs in O(nn log n+m log n) time. It is shown that skeletons of quasi-median graphs are median graphs. For an arbitrary vertex s an s-skeleton of a graph is obtained from G by deleting all edges uv that satisfy d(u, s) = d(v, s). As a by-product of this approach the size of a maximum complete subgraph of a quasi-median graph can be computed within the same time bound. Furthermore, we show that the distance matrix of a quasi-median graph can be computed in O(n 2).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.