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A computerised classification of some almost 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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(English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-151218OAI: oai:DiVA.org:su-151218DiVA, id: diva2:1172269
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt683",{id:"formSmash:j_idt683",widgetVar:"widget_formSmash_j_idt683",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt693",{id:"formSmash:j_idt693",widgetVar:"widget_formSmash_j_idt693",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt705",{id:"formSmash:j_idt705",widgetVar:"widget_formSmash_j_idt705",multiple:true}); Available from: 2018-01-09 Created: 2018-01-09 Last updated: 2018-01-09
##### In thesis

A graph G is called a (3,j;n)-minimal Ramsey graph if it has the least amount of edges, e(3,j;n), given that G is triangle-free, the independence number α(G)<j and that G has n vertices. Triangle-free graphs G with α(G)<j and where e(G)−e(3,j;n) is small are said to be almost minimal Ramsey graphs. We look at a construction of some almost minimal Ramsey graphs, called H₁₃-patterned graphs. We make computer calculations of the number of almost minimal Ramsey triangle-free graphs that are H₁₃-patterned. The results of these calculations indicate that many of these graphs are in fact H₁₃-patterned. In particular, all but one of the connected (3,j;n)-minimal Ramsey graphs for j≤9 are indeed H₁₃-patterned.

1. On minimal triangle-free Ramsey graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1172282",{id:"formSmash:j_idt1313:0:j_idt1322",widgetVar:"overlay1172282",target:"formSmash:j_idt1313:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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