Geodesic
Circular chromatic number of planar graphs of large odd girth
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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It was conjectured by Jaeger that $4k$-edge connected graphs admit a $(2k+1, k)$-flow. The restriction of this conjecture to planar graphs is equivalent to the statement that planar graphs of girth at least $4k$ have circular chromatic number at most $2+ {{1}\over {k}}$. Even this restricted version of Jaeger's conjecture is largely open. The $k=1$ case is the well-known Grötzsch 3-colour theorem. This paper proves that for $k \geq 2$, planar graphs of odd girth at least $8k-3$ have circular chromatic number at most $2+{{1}\over {k}}$.
DOI : 10.37236/1569
Classification : 05C15
Mots-clés : planar graphs, girth, circular chromatic number 
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     author = {Xuding Zhu},
     title = {Circular chromatic number of planar graphs of large odd girth},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1569},
     zbl = {0969.05022},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1569/}
}
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Xuding Zhu. Circular chromatic number of planar graphs of large odd girth. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1569

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