CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt166",{id:"formSmash:upper:j_idt166",widgetVar:"widget_formSmash_upper_j_idt166",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt167_j_idt170",{id:"formSmash:upper:j_idt167:j_idt170",widgetVar:"widget_formSmash_upper_j_idt167_j_idt170",target:"formSmash:upper:j_idt167:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On minimal triangle-free Ramsey graphsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Department of Mathematics, 2017. , p. 108
##### National Category

Discrete Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-151219OAI: oai:DiVA.org:su-151219DiVA, id: diva2:1172282
##### Presentation

2018-01-16, Room 306, House 6, Kräftriket 6, 104 05, Stockholm, 15:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt498",{id:"formSmash:j_idt498",widgetVar:"widget_formSmash_j_idt498",multiple:true}); Available from: 2018-01-11 Created: 2018-01-09 Last updated: 2018-01-11Bibliographically approved
##### List of papers

A graph G is called a minimal Ramsey (3, k; n)-graph if it has the least amount of edges, e(3, k; n), possible given that G is triangle-free, has independence number α(G) < k an has n vertices. The numbers e(3, k; n) and the minimalRamsey graphs are directly related to the Ramsey numbers R(3, k).This licentiate thesis studies minimal Ramsey graphs, graphs that are closeto being minimal Ramsey graphs and the edge numbers e(3, k; n) from several different aspects. Lower bounds on e(3, k; n) are lower bounds on the numberof edges in triangle-free graphs. In Paper I we show the bound

e(G) ≥ (1/3)(17n(G) − 35α(G) − N(C 4 ; G)),

where N(C4 ; G) that is number of cycles of length four in G. We also classifyall triangle-free graphs which satisfy this bound with equality.

In Paper II we study constructions of minimal Ramsey graphs, and graphsG such that e(G) − e(3, k; n) is small. We use a way to describe some of these graphs in terms of “patterns” and a recursive procedure to construct them. We also present the result of computer calculations where we have actually performed such constructions of Ramsey graphs and compare these lists to other computations of Ramsey graphs.

1. An invariant for minimum triangle-free graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1172267",{id:"formSmash:j_idt548:0:j_idt553",widgetVar:"overlay1172267",target:"formSmash:j_idt548:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. A computerised classification of some almost minimal triangle-free Ramsey graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1172269",{id:"formSmash:j_idt548:1:j_idt553",widgetVar:"overlay1172269",target:"formSmash:j_idt548:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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