# Browse Dissertations and Theses - Mathematics by Contributor "Furedi, Zoltan"

• (2004)
We also show that lambda(G) = q 2 + q = Delta2 - Delta for the incidence graph G of the projective plane PG (2, q). To prove this result, we convert the problem to a problem of packing of bipartite graphs into a complete ...

application/pdf

PDF (3MB)
• (2012-05-22)
In this thesis we study some extremal problems related to colorings and list colorings of graphs and hypergraphs. One of the main problems that we study is: What is the minimum number of edges in an $r$-uniform hypergraph ...

application/pdf

PDF (502kB)
• (2011-08-26)
In this thesis we consider several extremal problems for graphs and hypergraphs: packing, domination, and coloring. Graph packing problems have many applications to areas such as scheduling and partitioning. We consider a ...

application/pdf

PDF (853kB)
• (2011-05-25)
This dissertation investigates several questions in extremal graph theory and the theory of graph minors. It consists of three independent parts; the first two parts focus on questions motivated by Turan's Theorem and ...

application/pdf

PDF (711kB)
• (2013-08-22)
We study several extremal problems in graph labelling and in weak diameter of digraphs. In Chapter 2 we apply the Discharging Method to prove the 1,2,3-Conjecture [41] and the 1,2-Conjecture [48] for graphs with maximum ...

application/pdf

PDF (1MB)
• (1999)
The Ramsey-type coloring problems we consider include generalized Ramsey and generalized Anti-Ramsey problems. Namely, what is the minimal (or maximal) number of colors on the edges of a graph such that every subgraph ...

application/pdf

PDF (5MB)
• (2000)
A star, K1,s, is the complete bipartite graph whose partite sets have size 1 and s, respectively. A graph G has the t-star property if every t vertices of G belong to a subgraph which is a star. Erdo&huml;s, Sauer, Schaer, ...

application/pdf

PDF (5MB)
• (2005)
Finally, we also prove an analogue to the Erdo&huml;s-Ko-Rado Theorem on Hamming code.

application/pdf

PDF (2MB)
• (2011-01-14)
\noindent{This thesis focuses on topics in extremal combinatorics.} Given an integer-valued function $f$ defined on the vertices of a graph $G$, we say $G$ is {\em $f$-choosable} if for every collection of lists with ...

application/pdf

PDF (588kB)
• (2011-08-25)
We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number over $n$-vertex connected regular graphs in terms of ...

application/pdf

PDF (816kB)
• (2012-02-01)
We consider a variety of problems in extremal graph and set theory. Given a property $\Gamma$ and a family of sets ${\mathcal F}$, let $f({\mathcal F},\Gamma)$ be the size of the largest subfamily of ${\mathcal F}$ ...

application/pdf

PDF (531kB)
• (1999)
What is the maximum number of edges in a multigraph on n vertices if every k-set spans at most r edges? We asymptotically determine this maximum for almost all k and r as n tends to infinity, thus giving a generalization ...

application/pdf

PDF (5MB)
• (2010-08-20)
We consider a variety of problems in extremal graph and set theory. The {\em chromatic number} of $G$, $\chi(G)$, is the smallest integer $k$ such that $G$ is $k$-colorable. The {\it square} of $G$, written $G^2$, ...

application/pdf

PDF (484kB)
• (2012-02-06)
An H-immersion is a model of a graph H in a larger graph G. Vertices of H are represented by distinct "branch" vertices in G, while edges of H are represented by edge-disjoint walks in G joining branch vertices. By the ...

application/pdf

PDF (778kB)
• (2010-08-20)
Proving the existence or nonexistence of structures with specified properties is the impetus for many classical results in discrete mathematics. In this thesis we take this approach to three different structural questions ...

application/pdf

PDF (924kB)