Results 191 to 200 of about 3,787 (214)

Circular chromatic number of subgraphs

Journal of Graph Theory, 2003
AbstractThis paper proves that every (n + )‐chromatic graph contains a subgraph H with $\chi _c (H) = n$. This provides an easy method for constructing sparse graphs G with $\chi_c (G) = \chi ( G) = n$. It is also proved that for any ε > 0, for any fraction k/d > 2, there exists an integer g such that if G has girth at least g and $\chi _c (G ...
Hossein Hajiabolhassan, Xuding Zhu
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The circular chromatic number of the Mycielskian of Gdk

Journal of Graph Theory, 1999
In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph \(G\) into a new graph \(\mu (G)\), called the Mycielskian of \(G\), which has the same clique number as \(G\) and whose chromatic number equals \(\chi (G)+1\).
Lingling Huang, Gerard J. Chang
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Circular total chromatic numbers of graphs

Discrete Mathematics, 2016
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Cheyu Lin, Xuding Zhu
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On the circular chromatic number of graph powers

J. Graph Theory, 2014
Summary: This article intends to study some functors \(\mathcal F\) from the category of graphs to itself such that, for any graph \(G\), the circular chromatic number of \(\mathcal F (G)\) is determined by that of \(G\). In this regard, we investigate some coloring properties of graph powers.
Hossein Hajiabolhassan, Ali Taherkhani
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Graphs Whose Circular Chromatic Number Equals the Chromatic Number

Combinatorica, 1999
The circular chromatic number of a graph is the infimum (in fact, the minimum) of \({k}/{d}\) where there is a coloring \(f\) of the vertices with colors \(1,2,\dots,k\) in such a way that \(d\leq | f(x)-f(y)| \leq k-d\) holds when \(x\), \(y\) are adjacent.
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The circular chromatic number of series‐parallel graphs

Journal of Graph Theory, 1999
It is proved that if the girth of a series-parallel graph \(G\) is at least \(2 \lfloor (3k-1)/2 \rfloor\), then the circular chromatic number \(\chi_c(G)\) of \(G\) is at most \(4k/(2k-1)\).
Pavol Hell, Xuding Zhu
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Signed planar graphs with given circular chromatic numbers

Discrete Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yangyan Gu, Xuding Zhu
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Circular Chromatic Number and Mycielski Graphs

Combinatorica, 2004
Given positive integers \(k,d,\;k \geq 2d\), a \((k,d)\)-coloring of a graph \(G\) is a mapping \(c:\;V(G) \to \{0,1,\dots, k-1\}\) such that for each edge \(xy \in E(G)\), \(d \leq | c(x) - c(y)| \leq k-d\). The star chromatic number is defined as \(\chi^*(G) = \inf\{\frac{k}{d}: G\text{ has a }(k,d)\)-coloring\}, see \textit{A. Vince} [J.
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Circular chromatic number of hypergraphs.

Ars Comb., 2004
The notion of circular chromatic number of graphs was introduced by A. Vince in 1988: Let \(1\leq q < 2q\leq p\) be integers and let \(G=(V,E)\) be a graph. A map \(c:V\rightarrow [p]\) is a \((p,q)\)-coloring if \(q\leq | c(x)-c(y)| \leq p-q\) holds for each edge \(xy.\) The circular chromatic number \(\chi_c(G)=\inf {p \over q}\) (for all \((p,q ...
Changiz Eslahchi, Arash Rafiey
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The circular chromatic numbers of planar digraphs

Journal of Graph Theory, 2006
AbstractThe circular chromatic number is a refinement of the chromatic number of a graph. It has been established in [3,6,7] that there exists planar graphs with circular chromatic number r if and only if r is a rational in the set {1} ∪ [2,4]. Recently, Mohar, in [1,2] has extended the concept of the circular chromatic number to digraphs and it is ...
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