Adding Edges to Increase the Chromatic Number of a Graph

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333123" target="_blank" >RIV/00216208:11320/16:10333123 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0963548316000146" target="_blank" >http://dx.doi.org/10.1017/S0963548316000146</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0963548316000146" target="_blank" >10.1017/S0963548316000146</a>

Result language
angličtina
Original language name
Adding Edges to Increase the Chromatic Number of a Graph
Original language description
If n >= k + 1 and G is a connected n-vertex graph, then one can add k(k-1)/2 edges to G so that the resulting graph contains the complete graph K_{k+1}. This yields that for any connected graph G with at least k + 1 vertices, one can add k(k-1)/2 edges to G so that the resulting graph has chromatic number > k. A long time ago, Bollobas suggested that for every k >= 3 there exists a k-chromatic graph G(k) such that after adding to it any k(k-1)/2 - 1 edges, the chromatic number of the resulting graph is still k. In this note we prove this conjecture.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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