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Title:  Domination in Sparse Graphs 
Author(s):  Stodolsky, Burak Yildiran 
Doctoral Committee Chair(s):  West, Douglas B. 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  Given a partition pi of V (G) with parts ( V1, V2, ... , V t). A pidominating set B is a dominating set that is the union of parts of pi. The pidomination number gamma(G,pi) of G is the size of a smallest pidominating set. If each Vi in pi has size at most 2, we call pi a coupling of G and say that the vertices in Vi are coupled together. The coupled domination number, gamma cpl(G), is the maximum of gamma(G,pi) over all couplings pi of G. We also study coupled domination in trees. This topic was introduced by Slater and Seo, who established the coupled domination number of several different kinds of trees. They obtained a tree T' with gammacpl( T') = 8 and gamma(T' ) = 5. We show that gcplT gT ≥8/5 for every tree T with at least 2 vertices. 
Issue Date:  2008 
Type:  Text 
Language:  English 
Description:  69 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2008. 
URI:  http://hdl.handle.net/2142/86916 
Other Identifier(s):  (MiAaPQ)AAI3337932 
Date Available in IDEALS:  20150928 
Date Deposited:  2008 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois