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ChromaticPolynomial[g,k]

给出图 g 的色多项式.

ChromaticPolynomial[{vw,…},…]

使用规则 vw 来指定图 g.

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Details and Options Details and Options
范例  
基本范例  
范围  
应用  
属性和关系  
参见
相关指南
历史
按以下格式引用：

ChromaticPolynomial

ChromaticPolynomial[g,k]

给出图 g 的色多项式.

ChromaticPolynomial[{vw,…},…]

使用规则 vw 来指定图 g.

更多信息

范例

打开所有单元 关闭所有单元

基本范例  (1)

环图的色多项式：

Wolfram Language code: ChromaticPolynomial[CycleGraph[3], k]

绘制该多项式：

Wolfram Language code: DiscretePlot[%, {k, 20}]

范围  (6)

ChromaticPolynomial 适用于无向图：

Wolfram Language code: ChromaticPolynomial[[image], k]

有向图：

Wolfram Language code: ChromaticPolynomial[[image], k]

多重图：

Wolfram Language code: ChromaticPolynomial[[image], k]

混合图：

Wolfram Language code: ChromaticPolynomial[[image], k]

使用规则来指定图：

Wolfram Language code: ChromaticPolynomial[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}, k]

在指定值处计算：

Wolfram Language code: ChromaticPolynomial[[image], 3]

应用  (3)

计算 Petersen 图的3-着色数：

Wolfram Language code: ChromaticPolynomial[PetersenGraph[], 3]

求图的色数：

Wolfram Language code: p[k] = ChromaticPolynomial[PetersenGraph[], k]
Wolfram Language code: MinValue[{k, k > 0 && p[k] > 0 }, k, Integers]

具有 个顶点的完全图的色多项式：

Wolfram Language code: Table[ChromaticPolynomial[CompleteGraph[n], k], {n, 1, 7}]
Wolfram Language code: FindSequenceFunction[%, n]

环图：

Wolfram Language code: Table[ChromaticPolynomial[CycleGraph[n], k], {n, 1, 7}]
Wolfram Language code: FindSequenceFunction[%, n]

属性和关系  (3)

使用 TuttePolynomial 计算 ChromaticPolynomial：

Wolfram Language code: g = WheelGraph[5];
Wolfram Language code: {n, c} = {VertexCount[g], Length[ConnectedComponents[g]]};
Wolfram Language code: (-1)^n - ck^c * TuttePolynomial[g, {1 - k, 0}]//Expand
Wolfram Language code: ChromaticPolynomial[g, k]

当且仅当色多项式为 k(k-1)n-1 时，具有 个顶点的图是树：

Wolfram Language code: g = KaryTree[3];
Wolfram Language code: TreeGraphQ[g]
Wolfram Language code: {ChromaticPolynomial[g, k], k(k - 1)^VertexCount[g] - 1}//Expand

同构图具有相同的色多项式：

Wolfram Language code: g = [image];h = [image];
Wolfram Language code: IsomorphicGraphQ[g, h]
Wolfram Language code: ChromaticPolynomial[g, k] == ChromaticPolynomial[h, k]
Wolfram Research (2014)，ChromaticPolynomial，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ChromaticPolynomial.html （更新于 2015 年）.

文本

Wolfram Research (2014)，ChromaticPolynomial，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ChromaticPolynomial.html （更新于 2015 年）.

CMS

Wolfram 语言. 2014. "ChromaticPolynomial." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2015. https://reference.wolfram.com/language/ref/ChromaticPolynomial.html.

APA

Wolfram 语言. (2014). ChromaticPolynomial. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ChromaticPolynomial.html 年

BibTeX

@misc{reference.wolfram_2026_chromaticpolynomial, author="Wolfram Research", title="{ChromaticPolynomial}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/ChromaticPolynomial.html}", note=[Accessed: 06-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_chromaticpolynomial, organization={Wolfram Research}, title={ChromaticPolynomial}, year={2015}, url={https://reference.wolfram.com/language/ref/ChromaticPolynomial.html}, note=[Accessed: 06-September-2026]}