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Fractional total colourings of graphs of high girth
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Kaiser, Tomáš, King, Andrew D. and Králʼ, Daniel (2011) Fractional total colourings of graphs of high girth. Journal of Combinatorial Theory, Series B, Vol. 101 (No. 6). pp. 383-402. doi:10.1016/j.jctb.2010.12.005 ISSN 0095-8956.
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Official URL: http://dx.doi.org/10.1016/j.jctb.2010.12.005
Abstract
Reed conjectured that for every ϵ>0 and Δ there exists g such that the fractional total chromatic number of a graph with maximum degree Δ and girth at least g is at most Δ+1+ϵ. We prove the conjecture for Δ=3 and for even Δ⩾4 in the following stronger form: For each of these values of Δ, there exists g such that the fractional total chromatic number of any graph with maximum degree Δ and girth at least g is equal to Δ+1.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Combinatorial Theory, Series B | ||||
Publisher: | Elsevier Inc. | ||||
ISSN: | 0095-8956 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol. 101 | ||||
Number: | No. 6 | ||||
Page Range: | pp. 383-402 | ||||
DOI: | 10.1016/j.jctb.2010.12.005 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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