Irreversible k-threshold conversion processes on graphs

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dc.contributor.author Wodlinger, Jane
dc.date.accessioned 2018-04-30T16:37:58Z
dc.date.available 2018-04-30T16:37:58Z
dc.date.copyright 2018 en_US
dc.date.issued 2018-04-30
dc.identifier.uri https://dspace.library.uvic.ca//handle/1828/9282
dc.description.abstract Given a graph G and an initial colouring of its vertices with two colours, say black and white, an irreversible k-threshold conversion process on G is an iterative process in which a white vertex becomes permanently coloured black at time t if at least k of its neighbours are coloured black at time t-1. A set S of vertices is an irreversible k-threshold conversion set (k-conversion set) of G if the initial colouring in which the vertices of S are black and the others are white results in the whole vertex set becoming black eventually. In the case where G is (k+1)-regular, it can be shown that the k-conversion sets coincide with the so-called feedback vertex sets, or decycling sets. In this dissertation we study the size and structure of minimum k-conversion sets in several classes of graphs. We examine conditions that lead to equality and inequality in existing bounds on the minimum size of a k-conversion set of G, for k- and (k+1)-regular graphs G. Furthermore, we derive new sharp lower bounds on this number for regular graphs of degree ranging from k+1 to 2k-1 and for graphs of maximum degree k+1. We determine exact values of the minimum size of a k-conversion set for certain classes of trees. We show that every (k+1)-regular graph has a minimum k-conversion set that avoids certain structures in its induced subgraph. These results lead to new proofs of several known results on colourings and forest partitions of (k+1)-regular graphs and graphs of maximum degree k+1. en_US
dc.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject graph theory en_US
dc.subject conversion process en_US
dc.subject irreversible conversion process en_US
dc.subject k-conversion en_US
dc.subject decycling en_US
dc.subject feedback vertex en_US
dc.subject k-threshold en_US
dc.subject vertex arboricity en_US
dc.subject conversion set en_US
dc.subject forest partition en_US
dc.title Irreversible k-threshold conversion processes on graphs en_US
dc.type Thesis en_US
dc.contributor.supervisor Mynhardt, C.M.
dc.degree.department Department of Mathematics and Statistics en_US
dc.degree.level Doctor of Philosophy Ph.D. en_US
dc.description.scholarlevel Graduate en_US

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