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GALLAIRAMSEY NUMBERS FOR C7 WITH MULTIPLE COLORS
 Date Issued:
 2017
 Abstract/Description:
 The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. One view of this problem is in edgecolorings of complete graphs. For any graphs G, H1, ..., Hk, we write G ? (H1, ..., Hk), or G ? (H)k when H1 = ��� = Hk = H, if every kedgecoloring of G contains a monochromatic Hi in color i for some i ? {1,...,k}. The Ramsey number rk(H1, ..., Hk) is the minimum integer n such that Kn ? (H1, ..., Hk), where Kn is the complete graph on n vertices. Computing rk(H1, ..., Hk) is a notoriously difficult problem in combinatorics. A weakening of this problem is to restrict ourselves to Gallai colorings, that is, edgecolorings with no rainbow triangles. From this we define the GallaiRamsey number grk(K3,G) as the minimum integer n such that either Kn contains a rainbow triangle, or Kn ? (G)k . In this thesis, we determine the GallaiRamsey numbers for C7 with multiple colors. We believe the method we developed can be applied to find grk(K3, C2n+1) for any integer n ? 2, where C2n+1 denotes a cycle on 2n + 1 vertices.
Title:  GALLAIRAMSEY NUMBERS FOR C7 WITH MULTIPLE COLORS. 
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Name(s): 
Bruce, Dylan, Author Song, ZiXia, Committee Chair University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2017  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. One view of this problem is in edgecolorings of complete graphs. For any graphs G, H1, ..., Hk, we write G ? (H1, ..., Hk), or G ? (H)k when H1 = ��� = Hk = H, if every kedgecoloring of G contains a monochromatic Hi in color i for some i ? {1,...,k}. The Ramsey number rk(H1, ..., Hk) is the minimum integer n such that Kn ? (H1, ..., Hk), where Kn is the complete graph on n vertices. Computing rk(H1, ..., Hk) is a notoriously difficult problem in combinatorics. A weakening of this problem is to restrict ourselves to Gallai colorings, that is, edgecolorings with no rainbow triangles. From this we define the GallaiRamsey number grk(K3,G) as the minimum integer n such that either Kn contains a rainbow triangle, or Kn ? (G)k . In this thesis, we determine the GallaiRamsey numbers for C7 with multiple colors. We believe the method we developed can be applied to find grk(K3, C2n+1) for any integer n ? 2, where C2n+1 denotes a cycle on 2n + 1 vertices.  
Identifier:  CFH2000264 (IID), ucf:46025 (fedora)  
Note(s): 
20170501 B.S. College of Sciences, Mathematics Bachelors This record was generated from author submitted information. 

Subject(s): 
Combinatorics Ramsey Theory Graph Theory 

Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFH2000264  
Restrictions on Access:  public  
Host Institution:  UCF 