Fractional coloring of planar graphs of girth five

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10416991" target="_blank" >RIV/00216208:11320/20:10416991 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=w.0uC6mv_r" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=w.0uC6mv_r</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/18M1214068" target="_blank" >10.1137/18M1214068</a>

Result language
angličtina
Original language name
Fractional coloring of planar graphs of girth five
Original language description
A graph G is (a : b)-colorable if there exists an assignment of b-element subsets of {1, ..., a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph G and a vertex x is an element of V(G), the graph G has a set coloring phi by subsets of {1, ..., 6} such that vertical bar phi(v)vertical bar >= 2 for v is an element of V(G) and vertical bar phi(x)vertical bar = 3. As a corollary, every triangle-free planar graph on n vertices is (6n : 2n + 1)-colorable. We further use this result to prove that for every Delta, there exists a constant M-Delta such that every planar graph G of girth at least five and maximum degree Delta is (6M(Delta) : 2M(Delta) + 1)-colorable. Consequently, planar graphs of girth at least five with bounded maximum degree Delta have fractional chromatic number at most 3 -3/2M(Delta)+1.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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