Current Search: Davenport, Hunter M (x)


Title

ON SATURATION NUMBERS OF RAMSEYMINIMAL GRAPHS.

Creator

Davenport, Hunter M, Song, ZiXia, University of Central Florida

Abstract / Description

Dating back to the 1930's, Ramsey theory still intrigues many who study combinatorics. Roughly put, it makes the profound assertion that complete disorder is impossible. One view of this problem is in edgecolorings of complete graphs. For forbidden graphs H1,...,Hk and a graph G, we write G "arrows" (H1,...,Hk) if every kedgecoloring of G contains a monochromatic copy of Hi in color i for some i=1,2,...,k. If c is a (red, blue)edgecoloring of G, we say c is a bad coloring if G contains...
Show moreDating back to the 1930's, Ramsey theory still intrigues many who study combinatorics. Roughly put, it makes the profound assertion that complete disorder is impossible. One view of this problem is in edgecolorings of complete graphs. For forbidden graphs H1,...,Hk and a graph G, we write G "arrows" (H1,...,Hk) if every kedgecoloring of G contains a monochromatic copy of Hi in color i for some i=1,2,...,k. If c is a (red, blue)edgecoloring of G, we say c is a bad coloring if G contains no red K3or blue K1,t under c. A graph G is (H1,...,Hk)Ramseyminimal if G arrows (H1,...,Hk) but no proper subgraph of G has this property. Given a family F of graphs, we say that a graph G is Fsaturated if no member of F is a subgraph of G, but for any edge xy not in E(G), G + xy contains a member of F as a subgraph. Letting Rmin(K3, K1,t) be the family of (K3,K1,t)Ramsey minimal graphs, we study the saturation number, denoted sat(n,Rmin(K3,K1,t)), which is the minimum number of edges among all Rmin(K3,K1,t)saturated graphs on n vertices. We believe the methods and constructions developed in this thesis will be useful in studying the saturation numbers of (K4,K1,t)saturated graphs.
Show less

Date Issued

2018

Identifier

CFH2000291, ucf:45881

Format

Document (PDF)

PURL

http://purl.flvc.org/ucf/fd/CFH2000291