Multicolor Ramsey numbers for disjoint unions of graphs.
Item
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Title
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Multicolor Ramsey numbers for disjoint unions of graphs.
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Identifier
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AAI9108141
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identifier
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9108141
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Creator
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Loo, Saoping.
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Contributor
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Adviser: Stefan A. Burr
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Date
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1990
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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Let {dollar}G\sb1,G\sb2,\...,G\sb{lcub}\rm c{rcub}{dollar} be simple graphs, i.e., graphs without loops or multiple edges. The Ramsey number {dollar}r(G\sb1,G\sb2,\...,G\sb{lcub}\rm c{rcub}){dollar} is the smallest integer n such that if the edges of the complete graph {dollar}K\sb{lcub}n{rcub}{dollar} are colored arbitrarily with c colors, then for some i, the subgraph in color i contains a copy of {dollar}G\sb{lcub}i{rcub}{dollar}. Let mG denote m disjoint copies of some graph G. In this thesis we study the 3-color Ramsey numbers for large disjoint unions of graphs. Results are given which, in principle, permit the Ramsey numbers {dollar}r(n\sb1G\sb1,G\sb2,G\sb3){dollar}, {dollar}r(n\sb1G\sb1,n\sb2G\sb2,G\sb3){dollar}, and {dollar}r(n\sb1G\sb1,n\sb2G\sb2,n\sb3G\sb3){dollar} to be exactly evaluated when {dollar}G\sb{lcub}i{rcub}{dollar} are connected non-bipartite graphs, provided that the {dollar}n\sb{lcub}i{rcub}{dollar} are sufficiently large. Such evaluations are often possible in practice, as shown by several examples. For instance, when {dollar}n\sb1,n\sb2,n\sb3{dollar} are sufficiently large, {dollar}r(n\sb1K\sb3,n\sb2K\sb3,n\sb3K\sb3){dollar} = {dollar}3(n\sb1 + n\sb2{dollar} + {dollar}n\sb3){dollar}. Also in this thesis, when n is sufficiently large, results are given which, in principle, permit the Ramsey numbers r(nF,nG,nH) to be evaluated exactly for a large class of connected graphs, F, G, and H, where, some or all of these graphs may be bipartite.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
