Backbone Colorings and Generalized Mycielski Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00206481" target="_blank" >RIV/00216208:11320/09:00206481 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Backbone Colorings and Generalized Mycielski Graphs
Original language description
For a graph G and its spanning tree T the backbone chromatic number, BBC(G, T), is defined as the minimum k such that there exists a coloring c: V(G) -} {1, 2,..., k} satisfying |c(u)-c(v)| }= 1 if uv is an element of E(G) and |c(u)-c(v)| }= 2 if uv is an element of E(T). Broersma et al. [J. Graph Theory, 55 (2007), pp. 137-152] asked whether there exists a constant c such that for every triangle-free graph G with an arbitrary spanning tree T the inequality BBC(G, T) {= chi(G) c holds. We answer this question negatively by showing the existence of triangle-free graphs R_n and their spanning trees T_n such that BBC(R-n, T-n) = 2 chi(R-n)-1 = 2n-1. In order to answer the question, we obtain a result of independent interest. We modify the well-known Mycielski construction and construct triangle-free graphs J(n) for every integer n, with chromatic number n and 2-tuple chromatic number 2n (here 2 can be replaced by any integer t).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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