超立方体的r-Hued染色（英文）

冯博文; 熊玮

doi:10.13568/j.cnki.651094.651316.2023.12.25.0003

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超立方体的r-Hued染色（英文）

数理科学 | 更新时间：2026-01-21

- 超立方体的r-Hued染色（英文）
- 超立方体的r-Hued染色（英文）
- 新疆大学学报（自然科学版中英文） 2024年41卷第6期页码：651-656
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region of China “Spanning connectivity and supereulerian properties of graphs”(2022D01C410)
- DOI：10.13568/j.cnki.651094.651316.2023.12.25.0003
  中图分类号： O157.5
- 纸质出版：2024
- 稿件说明：
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[1]冯博文,熊玮.超立方体的r-Hued染色（英文）[J].新疆大学学报(自然科学版中英文),2024,41(06):651-656+686.
[1]冯博文,熊玮.超立方体的r-Hued染色（英文）[J].新疆大学学报(自然科学版中英文),2024,41(06):651-656+686. DOI： 10.13568/j.cnki.651094.651316.2023.12.25.0003.

DOI：10.13568/j.cnki.651094.651316.2023.12.25.0003.

摘要

对于正整数k和r

图G的一个(k

r)-染色是指图G中顶点的一个正常k-染色

并且每个顶点v的领域有至少dG(v)或r种不同颜色.图G的r-hued染色数是最小的整数k使得G有一个(k

r)-染色

记作χr(G).令Qn为n维超立方体.对于任意整数n和r

其中n≥2

2≤r≤5

研究了χr(Qn)

并确定了χ2(Qn)和χ3(Qn)对于所有正整数n的精确值.

Abstract

For positive integers k and r

a(k

r)-coloring of graph G is a proper vertex k-coloring of G such that the neighbors of any vertex v ∈ V(G) receive at least min{dG(v)

r} different colors. The r-hued chromatic number of G

denoted χr(G)

is the smallest integer k such that G admits a(k

r)-coloring. Let Qn be the n-dimensional hypercube. For any integers n and r with n ≥ 2 and 2 ≤ r ≤ 5

we investigated the behavior of χr(Qn)

and determined the exact value of χ2(Qn) and χ3(Qn) for all positive integers n.

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references

CHEN Y,FAN S H,LAI H J,et al.Graphr-hued colorings:A survey[J].Discrete Applied Mathematics,2022,321:24-48.

AKBARI S,GHANBARI M,JAHANBEKAM S.On the dynamic coloring of Cartesian product graphs[J].Ars Combinatoria,2014,114:161-168.

JAHANBEKAM S,KIM J,SUIL O,et al.Onr-dynamic coloring of graphs[J].Discrete Applied Mathematics,2016,206:65-72.

SUIL O. Matchings,connectivity,and eigenvalues in regular graphs[D].Illinois:University of Illinois at Urbana-Champaign,2011.

SHAO R F,ZUO L C.r-hued coloring of cartesian product of path with its square[J].Advances in Mathematics,2019,48(1):21-28.

LAI H J,LIN J L,MONTGOMERY B,et al.Conditional colorings of graphs[J].Discrete Mathematics,2006,306(16):1997-2004.

RIX J G.Hypercube coloring and the structure of binary codes[D].Vancouver:University of British Columbia,2008.

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