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Topics in graph fall-coloring.

Illinois Institute of Technology.

Topics in graph fall-coloring.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topics in graph fall-coloring.
作者:	Mitillos, Christodoulos.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2016
面頁冊數:	94 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
附註:	Adviser: Hemanshu Kaul.
Contained By:	Dissertation Abstracts International78-03B(E).
標題:	Applied mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10174175
ISBN:	9781369287011

Topics in graph fall-coloring.
Mitillos, Christodoulos.

Topics in graph fall-coloring. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 94 p.

Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.

Thesis (Ph.D.)--Illinois Institute of Technology, 2016.

Graph fall-coloring, also known as idomatic partitioning or independent domatic partitioning of graphs, was formally introduced by Dunbar, Hedetniemi, Hedetniemi, Jacobs, Knisely, Laskar, and Rall in 2000 as a simple extension of graph coloring and graph domination. It asks for a partition of the vertex set of a given graph into independent dominating sets.

ISBN: 9781369287011Subjects--Topical Terms:

377601
Applied mathematics.

Topics in graph fall-coloring.
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520 $a Graph fall-coloring, also known as idomatic partitioning or independent domatic partitioning of graphs, was formally introduced by Dunbar, Hedetniemi, Hedetniemi, Jacobs, Knisely, Laskar, and Rall in 2000 as a simple extension of graph coloring and graph domination. It asks for a partition of the vertex set of a given graph into independent dominating sets.
520 $a In this thesis, we will study a number of questions related to this concept. In the first chapter we will give a brief background to graph theory, and introduce the topic of graph fall-coloring, after looking at the fundamental topics it builds on. In the second chapter, we identify the effects on fall-colorability of various graphical operators, and look at the fall-colorability of certain families of graphs. In the third chapter we will explore certain constructions which create fall-colorable graphs given certain restrictions, and look at the interaction of fall-colorings and non-fall-colorings. Finally, in the fourth chapter, we lay the foundations to establish a connection between fall-coloring and certain existing open problems in graph theory, providing new possible avenues for exploring their solutions. We then provide two applied problems which can be solved with fall-coloring, and which motivate the notion of fall-near-coloring. We also provide further questions in fall-coloring for future research.
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