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Friendly and Unfriendly k-Partitions

Edmonds, Rex W
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1420640472

Abstract Details

2014, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
A friendly partition of a graph is a partition of the vertices into two sets so that every vertex has at least as many neighbors (adjacent vertices) in its own set as in the other set. An unfriendly partition of a graph is a partition of the vertices into two sets so that every vertex has at least as many neighbors in the other set as in its own set. In this paper we extend these concepts to k-partitions of vertices. We define and explore friendly and unfriendly edge partitions and extend these concepts to k-partitions of edges. In extending these concepts to the edges of a graph, we will show that one type of a friendly vertex partition of a Km,n graph can be used to produce a friendly edge partition. We will also look at partitions that are both friendly and unfriendly (dual). We will investigate these properties for several types of graphs (star, tree, Kn, Cn, Km,n).
Anita O'Mellan, PhD (Advisor)
Eric Wingler, PhD (Committee Member)
Jacek Fabrykowski, PhD (Committee Member)
43 p.
Mathematics; Theoretical Mathematics
Friendly and unfriendly vertex and edge partitions; Dual partitions; Constant edge partitions; m-cycles

Recommended Citations

Citations

  • Edmonds, R. W. (2014). Friendly and Unfriendly k-Partitions [Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1420640472

    APA Style (7th edition)

  • Edmonds, Rex. Friendly and Unfriendly k-Partitions. 2014. Youngstown State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ysu1420640472.

    MLA Style (8th edition)

  • Edmonds, Rex. "Friendly and Unfriendly k-Partitions." Master's thesis, Youngstown State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1420640472

    Chicago Manual of Style (17th edition)

ysu1420640472
454
© 2014, all rights reserved.
This open access ETD is published by Youngstown State University and OhioLINK.