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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

2016

University of South Carolina

Mathematics

Problems

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Full-Text Articles in Physical Sciences and Mathematics

Some Extremal And Structural Problems In Graph Theory, Taylor Mitchell Short Jan 2016

Some Extremal And Structural Problems In Graph Theory, Taylor Mitchell Short

Theses and Dissertations

This work considers three main topics. In Chapter 2, we deal with König-Egerváry graphs. We will give two new characterizations of König-Egerváry graphs as well as prove a related lower bound for the independence number of a graph. In Chapter 3, we study joint degree vectors (JDV). A problem arising from statistics is to determine the maximum number of non-zero elements of a JDV. We provide reasonable lower and upper bounds for this maximum number. Lastly, in Chapter 4 we study a problem in chemical graph theory. In particular, we characterize extremal cases for the number of maximal matchings in …