Universality in graph properties allowing constrained growth

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dc.contributor.author Broere, Izak
dc.contributor.author Heidema, Johannes
dc.date.accessioned 2020-09-28T15:41:07Z
dc.date.available 2020-09-28T15:41:07Z
dc.date.issued 2020
dc.description.abstract A graph property is a class of graphs which is closed under isomorphisms. Some properties are also closed under one or more specified constructions that extend any graph into a supergraph containing the original graph as an induced subgraph.We introduce and study in particular the concept that a property P “allows finite spiking” and show that there is a universal graph in every induced-hereditary property of finite character which allows finite spiking. We also introduce the concept that P “allows isolated vertex addition” and constructively show that there is a unique graph with the so-called P-extension property in every induced-hereditary property P of finite character which allows finite spiking and allows isolated vertex addition; such a graph is then universal in P too. Infinitely many examples which satisfy the conditions of both these results are obtained by taking the property of Kn-free graphs for an arbitrary integer n ≥ 2. en_ZA
dc.description.department Mathematics and Applied Mathematics en_ZA
dc.description.librarian am2020 en_ZA
dc.description.sponsorship The National Research Foundation of South Africa en_ZA
dc.description.uri http://www.elsevier.com/locate/akcej en_ZA
dc.identifier.citation I. Broere and J. Heidema, Universality in graph properties allowing constrained growth, AKCE International Journal of Graphs and Combinatorics (2019), https://DOI.org/ 10.1016/j.akcej.2019.02.002. NYP. en_ZA
dc.identifier.issn 0972-8600 (print)
dc.identifier.issn 2543-3474 (online)
dc.identifier.other 10.1016/j.akcej.2019.02.002
dc.identifier.uri http://hdl.handle.net/2263/76251
dc.language.iso en en_ZA
dc.publisher Elsevier en_ZA
dc.rights © 2019 Kalasalingam University. This is an open access article under the CC BY-NC-ND license. en_ZA
dc.subject Countable graph en_ZA
dc.subject Property of graphs en_ZA
dc.subject Universal graph en_ZA
dc.subject Finite character en_ZA
dc.subject Spiking en_ZA
dc.title Universality in graph properties allowing constrained growth en_ZA
dc.type Article en_ZA


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