colouring edges with many colours in cycles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286658" target="_blank" >RIV/00216208:11320/14:10286658 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jctb.2014.06.002" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2014.06.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2014.06.002" target="_blank" >10.1016/j.jctb.2014.06.002</a>

Result language
angličtina
Original language name
colouring edges with many colours in cycles
Original language description
The arboricity of a graph G is the minimum number of colours needed to colour the edges of G so that every cycle gets at least two colours. Given a positive integer p, we define the generalized p-arboricity Arbp(G) of a graph G as the minimum number of colours needed to colour the edges of a multigraph G in such a way that every cycle C gets at least min(|C|,p+1) colours. In the particular case where G has girth at least p+1 p+1, Arbp(G) is the minimum size of a partition of the edge set of G such thatthe union of any p parts induces a forest. In this paper, we relate the generalized p-arboricity of a graph G to the maximum density of a multigraphs having a shallow subdivision (where edges are becoming paths of length at most p) as a subgraph of G, byproving that each of these values is bounded by a polynomial function of the other.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
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
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)