Lattices of hereditary properties of nite graphs have been extensively studied. We investigate the lattice L of induced-hereditary
properties of countable graphs. Of interest to us will be some of
the members of L. Much of our focus will be on hom-properties. We analyze their behaviour and consider their link to solving
the long standing Hedetniemi Conjecture. We then discuss universal
graphs and construct a universal graph for hom-properties.
We then use these universal graphs to prove a theorem by Szekeres and
Wilf. Lastly we off er a new proof of a theorem by Du ffus, Sands and
Woodrow. / Dissertation (MSc)--University of Pretoria, 2013. / Mathematics and Applied Mathematics / Unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/33313 |
| Date | January 2013 |
| Creators | Matsoha, Moroli David Vusi |
| Contributors | Broere, Izak, moroli.matsoha@up.ac.za, Vetrik, Tomas |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Rights | © 2013 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
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