K4-free graphs with no odd hole: Even pairs and the circular chromatic number

2010 ◽  
Vol 65 (4) ◽  
pp. 303-322 ◽  
Author(s):  
Yori Zwols
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number ◽  
Even Pairs

scholarly journals T-colorings, divisibility and circular chromatic number

2021 ◽  
Vol 41 (2) ◽  
pp. 441
Author(s):  
Robert Janczewski ◽  
Anna Maria Trzaskowska ◽  
Krzysztof Turowski
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number

scholarly journals Circular chromatic number and Mycielski construction

2003 ◽  
Vol 44 (2) ◽  
pp. 106-115 ◽  
Author(s):  
Hossein Hajiabolhassan ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number

scholarly journals Construction of Kn-minor free graphs with given circular chromatic number

2003 ◽  
Vol 263 (1-3) ◽  
pp. 191-206 ◽  
Author(s):  
Sheng-Chyang Liaw ◽  
Zhishi Pan ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number ◽  
Minor Free Graphs

On the Circular Chromatic Number of Graph Powers

2013 ◽  
Vol 75 (1) ◽  
pp. 48-58 ◽  
Author(s):  
Hossein Hajiabolhassan ◽  
Ali Taherkhani
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number

scholarly journals The circular chromatic number of hypergraphs

2009 ◽  
Vol 309 (18) ◽  
pp. 5757-5765
Author(s):  
Richard C. Brewster ◽  
Gary MacGillivray ◽  
Laura Shepherd
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number

scholarly journals Density of universal classes of series-parallel graphs

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Jaroslav Nešetřil ◽  
Yared Nigussie
Keyword(s):  
Partial Order ◽  
Chromatic Number ◽  
Rational Number ◽  
Free Graph ◽  
Circular Chromatic Number ◽  
Density Result ◽  
Proper Subclass ◽  
International Audience ◽  
Universal Classes ◽  
Minor Free Graphs

International audience A class of graphs $\mathcal{C}$ ordered by the homomorphism relation is universal if every countable partial order can be embedded in $\mathcal{C}$. It was shown in [ZH] that the class $\mathcal{C_k}$ of $k$-colorable graphs, for any fixed $k≥3$, induces a universal partial order. In [HN1], a surprisingly small subclass of $\mathcal{C_3}$ which is a proper subclass of $K_4$-minor-free graphs $(\mathcal{G/K_4)}$ is shown to be universal. In another direction, a density result was given in [PZ], that for each rational number $a/b ∈[2,8/3]∪ \{3\}$, there is a $K_4$-minor-free graph with circular chromatic number equal to $a/b$. In this note we show for each rational number $a/b$ within this interval the class $\mathcal{K_{a/b}}$ of $0K_4$-minor-free graphs with circular chromatic number $a/b$ is universal if and only if $a/b ≠2$, $5/2$ or $3$. This shows yet another surprising richness of the $K_4$-minor-free class that it contains universal classes as dense as the rational numbers.

scholarly journals Circular Chromatic Number of Planar Graphs of Large Odd Girth

10.37236/1569 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Planar Graphs ◽  
Circular Chromatic Number ◽  
Connected Graphs ◽  
Restricted Version

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 $2+{{1}\over {k}}$.

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