Current Search: Combinatorics (x)
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Title
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GALLAI-RAMSEY NUMBERS FOR C7 WITH MULTIPLE COLORS.
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Creator
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Bruce, Dylan, Song, Zi-Xia, University of Central Florida
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Abstract / Description
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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 edge-colorings of complete graphs. For any graphs G, H1, ..., Hk, we write G ? (H1, ..., Hk), or G ? (H)k when H1 = ��� = Hk = H, if every k-edge-coloring of G contains a monochromatic Hi in color i for some i ? {1,...,k}. The Ramsey number rk(H1, ..., Hk) is the...
Show moreThe 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 edge-colorings of complete graphs. For any graphs G, H1, ..., Hk, we write G ? (H1, ..., Hk), or G ? (H)k when H1 = ��� = Hk = H, if every k-edge-coloring 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, edge-colorings with no rainbow triangles. From this we define the Gallai-Ramsey 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 Gallai-Ramsey 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.
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Date Issued
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2017
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Identifier
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CFH2000264, ucf:46025
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Format
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Document (PDF)
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PURL
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http://purl.flvc.org/ucf/fd/CFH2000264
